BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Gaia Comaschi (University of Campinas)
DTSTART:20200415T183000Z
DTEND:20200415T193000Z
DTSTAMP:20260404T095356Z
UID:BRAG/1
DESCRIPTION:Title: GIT stability of linear systems of skew-symmetric forms\nby Gaia C
omaschi (University of Campinas) as part of Brazilian algebraic geometry s
eminar\n\n\nAbstract\nGiven a 6 dimensional vector space $W$\, we consider
$\\mathbb{P}(\\mathbb{C}^{n+1}\\otimes \\bigwedge ^2 W^*)$\, the projecti
ve space parameterizing n-dimensional linear systems of skew-symmetric for
ms on $W$. Since the group $SL(W)$ acts on $\\mathbb{P}(\\mathbb{C}^{n+1}\
\otimes \\bigwedge ^2 W^*)$\, Geometric Invariant Theory (GIT) provides a
notion of (semi)stability. In this talk I will introduce a criterion to de
tect the (semi)stability of linear systems of skew-symmetric forms and I w
ill then present how this criterion allows to obtain a complete classifica
tion of all stable linear systems having generic rank equal to 4.\n\nAcces
s the Zoom link\nhttps://zoom.us/j/92887438541?pwd=Q3BHRU9CcFBicTJ1eXhacVp
LOERKUT09\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giosuè Muratore (Federal University of Minas Gerais (UFMG))
DTSTART:20200429T183000Z
DTEND:20200429T193000Z
DTSTAMP:20260404T095356Z
UID:BRAG/2
DESCRIPTION:Title: A Recursive Formula for Osculating Curves\nby Giosuè Muratore (Fe
deral University of Minas Gerais (UFMG)) as part of Brazilian algebraic ge
ometry seminar\n\n\nAbstract\nLet $X$ be a smooth complex projective varie
ty. Using a construction\ndevised to Gathmann\, we present a recursive for
mula for some of the\nGromov-Witten invariants of $X$. We prove that\, whe
n $X$ is homogeneous\, this\nformula gives the number of osculating ration
al curves at a general point of a general hypersurface of $X$. This genera
lizes the classical well known pairs of in inflection (asymptotic) lines f
or surfaces in $\\mathbb{P}^3$ of Salmon\, as well as Darboux's 27 osculat
ing conics.\n\nLink for the talk will be provided a few days in advance.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas das Dores (IMPA)
DTSTART:20200422T183000Z
DTEND:20200422T193000Z
DTSTAMP:20260404T095356Z
UID:BRAG/3
DESCRIPTION:Title: Schemes of rational curves on Del Pezzo surfaces\nby Lucas das Dor
es (IMPA) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nS
chemes parametrizing rational curves on a projective variety have a natura
l partition in terms of the degrees of the rational curves. In this talk\,
we present a natural refinement of this partition on schemes parametrizin
g rational curves on Del Pezzo surfaces. The classical description of Del
Pezzo surfaces as blow-ups of the projective plane at points in general po
sition yields that these refined partitions reflect the multiplicity of th
e rational curves at each of the blown-up points. Moreover\, we compute th
e dimension of components of these parameter spaces containing (points cor
responding to) resolutions of plane curves which are singular at the blown
-up points.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ugo Bruzzo (SISSA/UFPB)
DTSTART:20200513T183000Z
DTEND:20200513T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/5
DESCRIPTION:Title: About the McKay correspondence in 3 dimensions\nby Ugo Bruzzo (SIS
SA/UFPB) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nAb
stract: I will review work on the McKay correspondence in 3 dimensions and
its differential-geometric version\, relying on papers by Ito-Reid\, Sard
o Infirri\, Craw-Ishi and others\, and on some original results obtained w
ith a group of collaborators. This is about the resolution of singularitie
s of the type C^3/G\, where G is a finite subgroup of GL(3\,C) or SL(3\,C)
. I will also discuss the chamber structure for the stability parameter of
the GIT quotient. I will illustrate the general theory by means of a nont
rivial but manageable example (C^3/Z_4 with Z_4 acting as a subrgoup of SL
(3\,C)). I will also hint at some physical motivations.\n\nLink for the Zo
om meeting: https://us02web.zoom.us/j/84979113106?pwd=ZTc5c0N4WCtVdmdqbHNi
MzhiQU82QT09\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Almeida (Federal University of Minas Gerais (UFMG))
DTSTART:20200520T183000Z
DTEND:20200520T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/6
DESCRIPTION:Title: The geography of moduli spaces of torsion free sheaves\nby Charles
Almeida (Federal University of Minas Gerais (UFMG)) as part of Brazilian
algebraic geometry seminar\n\n\nAbstract\nIn this talk I will describe new
irreducible components of the moduli space of rank 2 semistable torsion f
ree sheaves on the 3-dimensional projective space\, whose generic point co
rresponds to non-locally free sheaves. As an application\, I will compute
the number of irreducible components of the moduli space of torsion free s
heaves\, with first\, second and third Chern classes equal to -1\, 2 and 2
respectively. Additionaly\, I will give an idea of how to prove that this
moduli space is connected. This is a joint work with Marcos Jardim and Al
exander S. Tikhomirov.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Fonseca (University of Oxford)
DTSTART:20200603T183000Z
DTEND:20200603T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/7
DESCRIPTION:Title: From transcendental numbers to higher Ramanujan foliations\nby Tia
go Fonseca (University of Oxford) as part of Brazilian algebraic geometry
seminar\n\n\nAbstract\nI will explain how a problem in the theory of trans
cendental numbers leads to the construction of certain principal bundles o
ver moduli stacks of abelian varieties. Such bundles carry a natural horiz
ontal foliation whose corresponding differential equations generalize Rama
nujan's classical relations between Eisenstein series. I will then discuss
a result on the Zariski-density of the analytic leaves of this foliation.
\n\nGoogle meet link https://meet.google.com/wwv-sajj-fsn\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Vitório Pereira (IMPA)
DTSTART:20200527T183000Z
DTEND:20200527T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/8
DESCRIPTION:Title: Miyaoka's algebraicity criterion and variations\nby Jorge Vitório
Pereira (IMPA) as part of Brazilian algebraic geometry seminar\n\n\nAbstr
act\nI will review some old and new results/arguments on the \nalgebraicit
y of leaves of foliations with "positive" tangent \nsheaf.\n\nLink for goo
gle meet will be posted a few days in advance.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Herivelto Borges\, Saeed Tafazolian\, Luciane Quoos Conte and Cíc
ero Carvalho (Federal University of Minas Gerais (UFMG))
DTSTART:20200610T183000Z
DTEND:20200610T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/9
DESCRIPTION:Title: In honor of Fernando Torres\nby Herivelto Borges\, Saeed Tafazolia
n\, Luciane Quoos Conte and Cícero Carvalho (Federal University of Minas
Gerais (UFMG)) as part of Brazilian algebraic geometry seminar\n\n\nAbstra
ct\nOur esteemed colleague Fernando Torres passed away on May 28th 2020\,
aged 58. He completed his PhD at IMPA in 1993 under the supervision of Arn
aldo Garcia\, and was a professor at the University of Campinas since 1998
. He was widely known for his many contributions to the theory of algebrai
c curves over finite fields and its applications.\n\nThis memorial session
will have short presentations by Herivelto Borges\, Saeed Tafazolian\, Lu
ciane Quoos Conte and Cícero Carvalho and completed with testimonies by A
rnaldo Garcia\, and Torres's students\, collaborators and friends.\n\nLink
for google meet: meet.google.com/bve-gahp-ocn\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cecília Salgado (Federal University of Rio de Janeiro (UFRJ))
DTSTART:20200624T183000Z
DTEND:20200624T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/10
DESCRIPTION:Title: Mordell-Weil rank jumps and the Hilbert property\nby Cecília Sal
gado (Federal University of Rio de Janeiro (UFRJ)) as part of Brazilian al
gebraic geometry seminar\n\n\nAbstract\nLet X be an elliptic surface with
a section defined over a number field. Specialization theorems by Néron a
nd Silverman imply that the rank of the Mordell-Weil group of special fibe
rs is at least equal to the MW rank of the generic fiber. We say that the
rank jumps when the former is strictly larger than the latter. In this tal
k\, I will discuss rank jumps for elliptic surfaces fibred over the projec
tive line. If the surface admits a conic bundle we show that the subset of
the line for which the rank jumps is not thin in the sense of Serre. This
is joint work with Dan Loughran (Bath).\n\nLink for the google meet will
be posted here a few days before the talk.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Genival da Silva Junior (Imperial College)
DTSTART:20200617T183000Z
DTEND:20200617T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/11
DESCRIPTION:Title: Surfaces with Exceptional monodromy\nby Genival da Silva Junior (
Imperial College) as part of Brazilian algebraic geometry seminar\n\n\nAbs
tract\nThere have been several constructions of family of varieties with e
xceptional monodromy group. In most cases\, these constructions give Hodge
structures with high weight(Hodge numbers spread out). N. Katz was the fi
rst to obtain Hodge structures with low weight(Hodge numbers equal to (2\,
3\,2)) and geometric monodromy group G2. I this talk I will give an altern
ate description of Katz's result using Hodge theory.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:André Contiero (Federal University of Minas Gerais (UFMG))
DTSTART:20200701T183000Z
DTEND:20200701T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/12
DESCRIPTION:Title: Curves and Weierstrass points\nby André Contiero (Federal Univer
sity of Minas Gerais (UFMG)) as part of Brazilian algebraic geometry semin
ar\n\n\nAbstract\nIn this talk we will present some working in progress on
the moduli space of pointed curves with prescribed Weierstrass semigroup
at the marked point. We will present a tight lower bound for its dimension
when the semigroup is non-negatively graded\, and we will also give suffi
cient condition to its rationality when the semigroup is symmetric.\n\nLin
k for google meet will be posted here a few days in advance.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amar Henni (Federal University of Santa Catarina (UFSC))
DTSTART:20200722T183000Z
DTEND:20200722T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/13
DESCRIPTION:Title: On the fixed locus of framed instanton sheaves on $\\mathbb{P}^3$
\nby Amar Henni (Federal University of Santa Catarina (UFSC)) as part of B
razilian algebraic geometry seminar\n\n\nAbstract\nLet T be the three dime
nsional torus acting on $\\mathbb{P}^3$ and MT(c) be the fixed locus of th
e corresponding action on the moduli space of rank 2 framed instanton shea
ves on $\\mathbb{P}^3$. We show that MT(c) consist only of non locally-fre
e instanton sheaves whose double dual is the trivial bundle. Moreover\, we
relate these instantons to multiple structures and give a classification
of their support. This allows to compute a lower bound on the number of co
mponents of MT(c).\n\nLink for the google meet will be posted here a few d
ays before the talk.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Richster (Federal University of Itajubá (UNIFEI))
DTSTART:20200708T183000Z
DTEND:20200708T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/14
DESCRIPTION:Title: Secant defectiveness of toric varieties\nby Rick Richster (Federa
l University of Itajubá (UNIFEI)) as part of Brazilian algebraic geometry
seminar\n\n\nAbstract\nThe $h$-secant variety $Sec_{h}(X)$ of a non-degen
erate $n$-dimensional variety $X\\subset\\mathbb{P}^N$ is the Zariski clos
ure of the union of all linear spaces spanned by collections of $h$ points
of $X$.\nThe expected dimension of $Sec_{h}(X)$ is \n$Expdim(Sec_{h}(X)):
= \\min\\{nh+h-1\,N\\}$.\nThe actual dimension of $Sec_{h}(X)$ may be smal
ler than the expected one. \n\nLet $N$ be a rank $n$ free abelian group an
d $M$ its dual. Let $P\\subseteq M_{\\mathbb Q}$ be a full dimensional lat
tice polytope and $X_P$ the corresponding toric variety.\n\nIn this talk w
e discuss a new technique to give bounds on the Secant Defectivity of $X_P
$ using information from the polytope $P$. It is a joint work just submitt
ed with Antonio Laface and Alex Massarenti.\n\nThe link for the google mee
t will be posted here a few days in advance.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maral Mostafazadehfard (Federal University of Rio de Janeiro (UFRJ
))
DTSTART:20200715T183000Z
DTEND:20200715T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/15
DESCRIPTION:Title: Divisor class group of Hankel determinantal rings\nby Maral Mosta
fazadehfard (Federal University of Rio de Janeiro (UFRJ)) as part of Brazi
lian algebraic geometry seminar\n\n\nAbstract\nHankel determinantal rings
arise as homogeneous coordinate rings of higher order secant varieties of
rational normal curves. In any characteristic we give an explicit descript
ion of divisor class groups of these rings and as a consequence we show th
at they are $\\mathbb{Q}$-Gorenstein rings. It has been shown that each di
visor class group element is the class of a maximal Cohen Macaulay module.
\n\nBased on a joint work with Aldo Conca\, Anurag K. Singh and Matteo Var
baro.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Gondim (UFRPe)
DTSTART:20200812T183000Z
DTEND:20200812T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/16
DESCRIPTION:Title: Waring problems and the Lefschetz properties\nby Rodrigo Gondim (
UFRPe) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nWe s
tudy three variations of the Waring problem for homogeneous polynomials\,
concerning the Waring rank\, the border rank and the cactus rank of a form
. We show how the Lefschetz properties of the associated algebra affect th
em. The main tool is the theory of mixed Hessians and Macaulay-Matlis dual
ity. We construct new families of wild forms\, that is\, forms whose cactu
s rank\, of schematic nature\, is bigger then the border rank\, defined ge
ometrically.\n(Joint with T. Dias)\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Villaflor (IMPA)
DTSTART:20200805T183000Z
DTEND:20200805T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/17
DESCRIPTION:Title: Constructing algebraic cycles on hypersurfaces\, an explicit approach
to Hodge conjecture\nby Roberto Villaflor (IMPA) as part of Brazilian
algebraic geometry seminar\n\n\nAbstract\nHodge conjecture is one of the
major conjectures in algebraic geometry. In all the cases where Hodge conj
ecture has been verified\, no constructive proof has been given up to the
date. In other words there is no hint about how to construct an algebraic
cycle from a given Hodge cycle. In this talk we will consider this problem
in the case of hypersurfaces of the projective space. We will explain how
this question becomes more treatable when the Hodge cycle is given in a g
ood enough format in terms of Griffiths basis. Reducing the problem to con
structing these nice representatives of Hodge cycles. We will see some exa
mples where this approach works and highlight the difficulties that appear
in the general case.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Barbosa (Simons Center for Geometry and Physics)
DTSTART:20200729T183000Z
DTEND:20200729T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/18
DESCRIPTION:Title: String Dualities\, Higgs Bundles and $G_2$ Geometry\nby Rodrigo B
arbosa (Simons Center for Geometry and Physics) as part of Brazilian algeb
raic geometry seminar\n\n\nAbstract\nDualities in string/M theory often pr
ovide novel perspectives for deformation problems in geometry. In one such
instance\, involving Large $N$ duality in the B-model\, one can construct
a family of ALE-fibered Calabi-Yau threefolds over a Riemann surface $S_g
$ ($g \\geq 2$) whose Jacobian integrable system is isomorphic to the $G$-
Hitchin system over $S_g$\, where $G$ is the compact real form associated
to the ALE type via the McKay correspondence. I will explain a different p
hysical framework\, involving M-theory/Type IIA duality\, that gives an an
alogous construction of ALE-fibered $G_2$-manifolds parametrized by spectr
al covers of certain "smooth Higgs bundles" over a $3$-manifold. I will ex
plain how this theory connects with Donaldson's theory of Kovalev-Lefschet
z fibrations and how it presents a window for applying algebro-geometric t
echniques to moduli problems in $G_2$-geometry. Time permitting\, I will c
omment on a second algebro-geometric model for the moduli space of (comple
xified) $G_2$-structures derived from SYZ Mirror Symmetry for the Type IIA
geometry.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Esteves (IMPA)
DTSTART:20200902T183000Z
DTEND:20200902T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/19
DESCRIPTION:Title: Degenerations of line bundles along curves\nby Eduardo Esteves (I
MPA) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nA fami
ly of line bundles along a family of smooth curves parameterized by the pu
nctured disk can be extended in several ways over the limit stable curve o
f the family. We show that the collection of all extensions can be natural
ly parameterized by the torus quotient of the arrangement of toric varieti
es associated to a certain polytope decomposition of a certain Euclidean s
pace. We characterize all polytope decompositions arising this way in term
s of combinatorial data of the stable curve. At the end I will describe ho
w these results may be used to construct new compactifications of Jacobian
s of stable curves and address the problem raised by Eisenbud and Harris o
f constructing a useful moduli of limit linear series over the moduli of s
table curves. This is an ongoing joint work with Omid Amini (École Polyte
chnique).\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nuno Cardoso / Aline Zanardini (University of Miami / University o
f Pennsylvania)
DTSTART:20200826T183000Z
DTEND:20200826T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/20
DESCRIPTION:Title: Towards a new technique to compute Orlov spectra / Stability of Halph
en pencils of index two\nby Nuno Cardoso / Aline Zanardini (University
of Miami / University of Pennsylvania) as part of Brazilian algebraic geo
metry seminar\n\n\nAbstract\nTowards a new technique to compute Orlov spec
tra\, by Nuno Cardoso \n\nAbstract: A generator of a triangulated category
is an object from which we can obtain the whole category through certain
operations. Associated to a generator\, there is the notion of the generat
ion time\, which is the number describing how long the rebuilding process
takes. The generation time of the fastest generator is called the Rouquier
dimension of the category and it is conjectured that the Rouquier dimensi
on of the derived category of a smooth projective variety of dimension n i
s exactly n. Orlov suggested that in order to extract additional geometric
information from the category\, one should study all possible generation
times – the Orlov spectrum. Later\, Ballard\, Favero and Katzarkov devel
oped considerably our understanding of the topic\, making connections to r
ationality\, computing the Orlov spectrum in several cases and finding bou
nds for it. In this talk\, we will review part of their results and discus
s our work in progress on a new technique to compute the Orlov spectrum\,
which takes inspiration on Abouzaid's criterion for generating the Fukaya
category in terms of open-closed maps.\n\n--xx--xx--\n\nStability of Halph
en pencils of index two\, by Aline Zanardini\n\nAbstract: In this talk I w
ill present some results about the stability\, in the sense of geometric i
nvariant theory\, of Halphen pencils of index two under the action of SL(3
). These are pencils of plane curves of degree six having nine (possibly i
nfinitely near) base points of multiplicity two. Inspired by the work of M
iranda on pencils of plane cubics\, I will explain how to explore the geom
etry of the associated rational elliptic surfaces. I will also show that
the log canonical threshold plays an important role. This work is part of
my PhD thesis at the University of Pennsylvania under the supervision of A
ntonella Grassi.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Abreu (UFF)
DTSTART:20200819T183000Z
DTEND:20200819T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/21
DESCRIPTION:Title: A geometric interpretation for characters of Iwahori--Hecke algebras<
/a>\nby Alex Abreu (UFF) as part of Brazilian algebraic geometry seminar\n
\n\nAbstract\nThe Iwahori-Hecke algebra is a deformation of the group alge
bra of the symmetric group. It has a distinguished basis (enumerated by pe
rmutations) called the Kazhdan-Lusztig basis. For each permutation we con
sider certain subvarieties of the complete flag variety that generalize He
ssenberg varieties. These varieties carry an action of the symmetric group
on its intersection cohomology groups. We prove that the Frobenius chara
cter of this action is precisely the Frobenius character of an element of
the Kazhdan-Lusztig basis of the Hecke algebra. This is a generalization
to non-codominant permutations of Brosnan-Chow's solution to the Sharesia
n-Wachs conjecture. Some partial results in other Lie types are also achi
eved.\n\nLink for the google meet will be posted here a few days before th
e talk.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Muniz (UFF)
DTSTART:20200909T183000Z
DTEND:20200909T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/22
DESCRIPTION:Title: On moduli spaces of rank two logarithmic connections over an elliptic
curve.\nby Alan Muniz (UFF) as part of Brazilian algebraic geometry s
eminar\n\n\nAbstract\nWe will give an explicit description of the (coarse)
moduli space of rank two logarithmic connections with fixed spectral data
over an elliptic curve. Precisely\, we will show that this moduli space h
as a covering whose members are easily described.\n\nJoint work with Thiag
o Fassarella (UFF) and Frank Loray (IRMAR).\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Faenzi (Université de Bourgogne)
DTSTART:20200916T183000Z
DTEND:20200916T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/23
DESCRIPTION:Title: Stability of logarithmic tangents\nby Daniele Faenzi (Université
de Bourgogne) as part of Brazilian algebraic geometry seminar\n\n\nAbstra
ct\nTo a hypersurface $D$ of projective $N$-space $\\mathbb{P}^N$ one atta
ches the \\emph{log\ntangent sheaf} $T_D$ of vector fields of $\\mathbb{P}
^N$ tangent to D. For some highly\nspecial hypersurfaces\, such as\, for i
nstance\, hyperplane arrangements\nassociated to reflection groups and dis
criminants of binary forms\, the\nsheaf $T_D$ splits into line bundles -
$D$ is then called \\emph{free}. On the\nother hand\, Dolgachev--Kapranov
proved that $T_D$ is stable if $D$ is a\ngeneric arrangement of at least $
N+2$ hyperplanes\; also Dimca proved that\n$T_D$ is stable if $D$ has isol
ated singularities with sufficiently small\nTjurina number and $N=3$.\n\nI
n this talk we will first show that $T_D$ is stable for a much wider\nclas
s of hypersurfaces having low-dimensional singularities. In the\nsecond pa
rt of the talk we will prove that $T_D$ is stable if $D$ is the\ndetermina
nt of $n\\times n$ matrices.\nIf time allows\, we will discuss the applica
tion from the equisingular\nHilbert scheme containing $D$ to the moduli sp
ace of semistable sheaves\ncontaining $T_D$ and show that it is birational
in the case of determinants.\n\nThis is a report on work in progress with
S. Marchesi - soon on the arXiv.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessia Mandini (UFF)
DTSTART:20200923T183000Z
DTEND:20200923T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/24
DESCRIPTION:Title: Quasi-parabolic Higgs bundles and null hyperpolygon spaces\nby Al
essia Mandini (UFF) as part of Brazilian algebraic geometry seminar\n\n\nA
bstract\nHyperpolygons spaces are a family of hyperkähler manifolds\, tha
t can be obtained from coadjoint orbits by hyperkähler reduction. Jointly
with L. Godinho\, we showed that these spaces are isomorphic to certain f
amilies of parabolic Higgs bundles\, when a suitable condition between the
parabolic weights and the spectra of the coadjoint orbits is satisfied.\n
\nIn analogy to this construction\, we introduce two moduli spaces: the mo
duli spaces of quasi-parabolic $SL(2\,\\mathbb{C})$-Higgs bundles over $\\
mathbb{C}\\mathbb{P}^1$ on one hand and the null hyperpolygon spaces on th
e other\, and establish an isomorphism between them.\n\nFinally we describ
e the fixed loci of natural involutions defined on these spaces and relate
them to the moduli space of null hyperpolygons in the Minkowski 3-space.\
n\nThis is based on joint works with Leonor Godinho.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sally Andria / César Hilário (UFF / IMPA)
DTSTART:20200930T183000Z
DTEND:20200930T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/25
DESCRIPTION:Title: An explicit resolution of the Abel map via tropical geometry / Bertin
i’s theorem in positive characteristic\nby Sally Andria / César Hil
ário (UFF / IMPA) as part of Brazilian algebraic geometry seminar\n\n\nAb
stract\nAn explicit resolution of the Abel map via tropical geometry\, by
Sally Andria (UFF)\n\nIn this talk I will talk about the problem studied i
n my thesis: Is it possible to find an explicit resolution of the Abel map
(a rational map) for a nodal curve?\nWe start with a family of curves\, t
hat is a regular smoothing of a nodal curve with smooth components. We tak
e a polarization\, an invertible sheaf\, and a section through the smooth
locus of the family. The Abel map is the rational map taking a tuple of po
ints $(Q_1\,\\ldots\,Q_d)$ on a curve of the family to the associated shea
f in the Esteves compactified Jacobian. We translate this problem into an
explicit combinatorial problem by means of tropical and toric geometry. Th
e solution of the combinatorial problem gives rise to an explicit resoluti
on of the Abel map.\n\n\n-- xx -- xx --\n\nBertini’s theorem in positive
characteristic\, by Cesar Hilario (IMPA)\n\nA classical theorem of Bertin
i states that in characteristic zero almost all the fibers of a dominant m
orphism between two smooth algebraic varieties are smooth\, that is\, ther
e do not exist fibrations by singular varieties with smooth total space. U
nfortunately\, Bertini’s theorem fails in positive characteristic\, as w
as first observed by Zariski in the 1940s. Investigating such a failure na
turally leads to the classification of its exceptions. By a theorem of Tat
e\, a fibration by singular curves of arithmetic genus $g$ in characterist
ic $p > 0$ may exist only if $p \\le 2g + 1$. When $g = 1$ and $g = 2$\, t
hese fibrations have been studied by Queen\, Borges Neto\, Stohr and Simar
ra Cañate. A birational classification of the case $g = 3$ was started by
Stohr ($p = 7\, 5$)\, and then continued by Salomão ($p = 3$). In this t
alk I shall report on some progress in the case $g = 3$\, $p = 2$. In fact
\, several examples show already that in this setting very interesting geo
metric phenomena arise.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damiano Testa (University of Warwick)
DTSTART:20201007T183000Z
DTEND:20201007T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/26
DESCRIPTION:Title: Contact in algebraic and tropical geometry\nby Damiano Testa (Uni
versity of Warwick) as part of Brazilian algebraic geometry seminar\n\n\nA
bstract\nIn recent years\, classical enumerative problems in algebraic geo
metry have been converted into statements in tropical geometry. This appr
oach has had tremendous success. In view of the current pandemic\, we wil
l stay away from these popular results. Rather\, we discuss two isolated
cases: the 9 inflection points of plane cubics and the 28 bitangent lines
of plane quartics. The tropical counts yield 3 and 7\, respectively. We
will see how to reconcile these results via positive characteristic. These
cases naturally generalize to inflection points of plane curves of arbitr
ary degree and theta-characteristics of curves of general type.\n\nThe tal
k assumes minimal familiarity with basic concepts of algebraic geometry ov
er the complex numbers. Positive characteristic and tropical geometry play
important\, but non-technical roles. This is joint work with Marco Pacini
.\n\nLink for the talk will be posted here a few days before the talk.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Jardim (UNICAMP)
DTSTART:20201014T183000Z
DTEND:20201014T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/27
DESCRIPTION:Title: Classification of codimension one distributions of degree two on the
projective space\nby Marcos Jardim (UNICAMP) as part of Brazilian alg
ebraic geometry seminar\n\n\nAbstract\nIn this talk I will provide a compl
ete classification of codimension one distributions of degree 2 on the th
ree dimensional projective space\, generalizing the classification of cod
imension one foliations of degree 2 given by Cerveau and Lins Neto. We des
cribe all possible singular schemes and tangent sheaves of such distributi
ons and speculate on the topological and algebraic properties of integrabi
lity.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Douglas Guimarães (UNICAMP)
DTSTART:20201028T183000Z
DTEND:20201028T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/28
DESCRIPTION:Title: Moduli spaces of quasitrivial rank 2 sheaves\nby Douglas Guimarã
es (UNICAMP) as part of Brazilian algebraic geometry seminar\n\n\nAbstract
\nDouglas Guimarães (UNICAMP)\n\nTitle: Moduli spaces of quasitrivial ran
k 2 sheaves\n\nAbstract: A torsion free sheaf $E$ on $\\mathbb{P}^3$ is ca
lled quasitrivial if $E^{\\vee\\vee}=\\mathcal{O}_{\\mathbb{P}^3}^{\\oplus
r}$ and $\\dim(E^{\\vee\\vee}/E)=0$. While such sheaves are always $\\mu
$-semistable\, they may not be Gieseker semistable. We study the moduli sp
aces of $\\mu$- and Gieseker semistable quasitrivial sheaves of rank 2 vi
a the quot scheme of points $Quot(\\mathcal{O}_{\\mathbb{P}^3}^{\\oplus 2}
\,n)$\, where $n=h^0(E^{\\vee\\vee}/E)$. We will show the construction of
an irreducible component of the Gieseker moduli space which is birrational
to the total space of a $\\mathbb{P}^{n-1}$-bundle over $S(n-1)\\times\\m
athbb{P}^3$\, where $S(n)$ is the smoothable component of the Hilbert sche
me of $n$ points in $ \\mathbb{P}^3$. Furthermore\, this is the only irred
ucible component when $n\\le10$.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ageu Barbosa (UFPB)
DTSTART:20201021T183000Z
DTEND:20201021T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/29
DESCRIPTION:Title: On $(h\,s)$-tangential weak defectiveness and identifiability of some
projective varieties\nby Ageu Barbosa (UFPB) as part of Brazilian alg
ebraic geometry seminar\n\n\nAbstract\nIn this talk\, I will present a new
technique to study the problem of weak defectiveness using degenerations
of tangent linear spaces to osculating linear spaces. I also will present
a result on tangential weak defectiveness for varieties admitting a fibrat
ion with a linearly embedded $\\mathbb{P}^1$ as general fiber and apply it
to obtain a sharp asymptotic bound for non secant defectiveness of Segre
varieties.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Israel Vainsencher (UFMG)
DTSTART:20201104T183000Z
DTEND:20201104T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/30
DESCRIPTION:Title: Enumerative geometry of legendrian foliations\nby Israel Vainsenc
her (UFMG) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\n
Foliations\, or more generally\, distributions\, provide a geometric\nview
point in the theory of differential equations. Grosso modo\,\na foliation
of dimension one\, is a (polynomial) recipe to draw a line\nat each point.
We’ll stick to 3-dim projective space. Similarly\, a\ndistribution of c
odimension one assigns a plane at each point. We\nassume the coefficients
of the equation of the plane are of degree one.\nAs syzygies trained minds
will recognize\, this entails the distribution\nis specified by an anti-s
ymmetric 4×4 matrix. Those of maximal\nrank correspond to the distributio
ns of contact. A foliation is called\nlegendrian whenever tangent to some
distribution of contact. Our\ngoal is to describe the calculation of the d
imension and degree of\nthe subvariety of legendrian foliations (and frien
ds). It turns out that\nthe answer is given by Athus polynomials. This fit
s into a Schubert\nCalculus like programme of exploring the geometry of pa
rameter\nspaces of foliations.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Kleiman (MIT)
DTSTART:20210224T183000Z
DTEND:20210224T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/31
DESCRIPTION:Title: Geometry of Gorenstein Artinian Algebra\nby Steven Kleiman (MIT)
as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nMacaulay Du
ality\, between filtered quotients of a polynomial ring over\na field\, an
nihilated by a power of the variables\, and Artinian\nsubmodules of the ri
ng's graded dual\, is generalized over any Noetherian\nground ring\, and u
sed to provide isomorphisms between the subschemes of\nthe Hilbert scheme
parameterizing various sorts of these quotients\, and\nthe corresponding s
ubschemes of the Quot scheme of the dual. Notably\,\non this basis\, the
scheme of compressed Gorenstein algebras is proved to\nbe smooth and irred
ucible of a certain relative dimension. Joint work in progress with Jan Kl
eppe.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Gargiulo (IMPA)
DTSTART:20201111T183000Z
DTEND:20201111T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/32
DESCRIPTION:Title: Rational pullbacks of toric foliations\nby Javier Gargiulo (IMPA)
as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nIn this ta
lk we will present a short digression about the theory of singular foliati
ons on toric varieties and certain algebraic spaces parametrizing them. In
particular\, we will construct families of singular foliations on a class
ical projective space that arise as pull-backs of foliations on a simplici
al toric variety X under suitable rational maps. We will focus on the ca
se where X is a complete simplicial toric surface.\n\nThe singular set of
a foliation is one of the most commonly studied geometric objects in the
area. The geometry and topology near a singularity characterize (in some s
ense) the foliation. Not surprisingly\, most of the approaches to obtain s
tability results for singular foliations involve a detailed study of their
singular locus. In this respect\, we will attempt to describe certain asp
ects of the singular and Kupka scheme of foliations on a toric surface and
their corresponding pull-backs. We will also characterize their first ord
er unfoldings and deformations in some cases.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Marchesi (Universitat de Barcelona)
DTSTART:20201118T183000Z
DTEND:20201118T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/33
DESCRIPTION:Title: Group actions on vector bundles\nby Simone Marchesi (Universitat
de Barcelona) as part of Brazilian algebraic geometry seminar\n\n\nAbstrac
t\nThe classification of vector bundles which are invariant under the acti
on of a determined group\, has been widely studied.\n\nWe can consider\, f
or example\, the canonical action of the projective linear group $PGL(n+1)
$ on $\\mathbb{P}^n$ which leads to the definition of homogeneous vector b
undle. The choice of specific subgroups has been often determined\, in lit
erature\, restricting our attention to particular families. Recall indeed
that Ancona and Ottaviani proved that the Steiner bundles on $\\mathbb{P}^
n$ that are invariant under an action of $SL(2\,\\mathbb{C})$ are the so c
alled Schwarzenberger bundles. Another example\, moving into the realm of
hyperplane arrangements\, in which I have been particularly interested lat
ely\, is given by the reflection arrangements. They are defined as hyperpl
ane arrangements that are invariant under the group generated by their ref
lections\, and it is known that their associated sheaf is free (a sum of l
ine bundles) and therefore homogeneous.\n \nIn a previous work\, studying
Nearly-free arrangements\, we proved that their configuration of jumping
lines is extremely special but remarked that it did not characterize this
family of arrangements. It turns out that they are characterized by the in
variance under the action of the subgroup $G_p \\subset \\mathrm{PGL}(3)$
that fixes the point $p$ in the projective plane. Inspired by this result
\, we classify vector bundles which are invariant under the action of subg
roups that fix linear subspaces of the projective plane.\n\nFinally\, we w
ill focus on the relations between the geometry of the jumping locus and t
he invariance under the action of the group. Recall that\, historically\,
such question has been studied in order to relate homogeneous bundles with
uniform ones\, i.e. bundles for which the splitting type is constant.\n \
nThis is the result of two collaborations: one with Jean Vallès and one w
ith Rosa Maria Miró-Roig.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lorscheid (IMPA)
DTSTART:20201125T183000Z
DTEND:20201125T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/34
DESCRIPTION:Title: The moduli space of matroids\nby Oliver Lorscheid (IMPA) as part
of Brazilian algebraic geometry seminar\n\n\nAbstract\nMatroids are combin
atorial gadgets that reflect properties of linear algebra in situations wh
ere this latter theory is not available. This analogy prescribes that the
moduli space of matroids should be a Grassmannian over a suitable base obj
ect\, which cannot be a field or a ring\; in consequence usual algebraic g
eometry does not provide a suitable framework. In joint work with Matt Bak
er\, we have used algebraic geometry over the so-called field with one ele
ment to construct such moduli spaces. As an application\, we streamline va
rious results of matroid theory and find simplified proofs of classical th
eorems\, such as the fact that a matroid is regular if and only if it is b
inary and orientable.\n\nWe will dedicate the first part of this talk to a
n exposition of matroids. Then we will briefly outline how to construct th
e moduli space of matroids. In a last part\, we will explain with some car
e why this theory is useful to simplify classical results in matroid theor
y.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA)
DTSTART:20201202T183000Z
DTEND:20201202T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/35
DESCRIPTION:Title: Birational geometry of Calabi-Yau pairs and 3-dimensional Cremona tra
nsformations\nby Carolina Araujo (IMPA) as part of Brazilian algebraic
geometry seminar\n\n\nAbstract\nRecently\, Oguiso addressed the following
question\, attributed to Gizatullin: ``Which automorphisms of a smooth qu
artic K3 surface $D\\subset \\PP^3$ are induced by Cremona transformations
of the ambient space $\\mathbb{P}^3$?'' \n\nWhen $D\\subset \\mathbb{P}^3
$ is a smooth quartic surface\, $(\\mathbb{P}^3\,D)$ is an example of a C
alabi-Yau pair\, that is\, a pair $(X\,D)$\, consisting of a normal projec
tive variety $X$ and an effective Weil divisor $D$ on $X$ such that $K_X+D
\\sim 0$. Gizatullin's question is about birational properties of the Cala
bi-Yau pair $(\\mathbb{P}^3\,D)$. In this talk\, I will explain a general
framework to study the birational geometry of mildly singular Calabi-Yau p
airs. Then I will focus on the case of singular quartic surfaces $D\\subse
t \\mathbb{P}^3$. Our results illustrate how the appearance of increasingl
y worse singularities in $D$ enriches the birational geometry of the pair
$(\\mathbb{P}^3\, D)$\, and lead to interesting subgroups of the Cremona g
roup of $\\mathbb{P}^3$.\n\nThis is joint work with Alessio Corti and Alex
Massarenti.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Martinez (UNICAMP)
DTSTART:20210303T183000Z
DTEND:20210303T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/36
DESCRIPTION:Title: Stability under Fourier-Mukai transforms on elliptic surfaces\nby
Cristian Martinez (UNICAMP) as part of Brazilian algebraic geometry semin
ar\n\n\nAbstract\nLet $X$ be a Weierstrass elliptic surface. By moving the
polarization towards the fiber direction while keeping the volume of the
polarization fixed\, we can define a notion of limit Bridgeland stability.
In this talk\, we will prove that under certain conditions the relative F
ourier--Mukai transform of a slope semistable sheaf is a limit semistable
object. In the case that the surface has Picard rank two\, a detailed stud
y of the potential Bridgeland walls will provide us with extra numerical c
onditions to guarantee that the Fourier--Mukai transform of a 1-dimensiona
l slope semistable sheaf is Bridgeland semistable.\n\nZoom Meeting ID: 913
6913 4478\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inder Kaur (PUC-Rio)
DTSTART:20210310T183000Z
DTEND:20210310T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/37
DESCRIPTION:Title: Questions on the cohomology ring of moduli spaces of stable locally-f
ree sheaves on curves\nby Inder Kaur (PUC-Rio) as part of Brazilian al
gebraic geometry seminar\n\n\nAbstract\nLet $M(2\,L)$ denote the moduli sp
ace of stable vector bundles of rank $2$ and determinant $L$ of odd degree
\, on a smooth curve of genus $g \\geq 2$. Owing to the work of Mumford\,
Newstead\, Kirwan\, King and several others\, questions such as the genera
tors and relations\, higher rank Torelli-type theorems as well as the Hodg
e conjecture for the cohomology ring of $M(2\,L)$ are well understood. In
this talk I will survey some of these aspects for the smooth case and disc
uss analogous results for the case when the underlying curve is irreducibl
e\, nodal. This is joint work with Suratno Basu and Ananyo Dan.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederico Quallbrunn (Universidad CAECE)
DTSTART:20210317T183000Z
DTEND:20210317T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/38
DESCRIPTION:Title: Unfoldings of Lie algebroids\nby Frederico Quallbrunn (Universida
d CAECE) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nWe
will talk about the notion of unfolding\, first on\nfoliations\, and then
generalizing this concept to the case of Lie\nalgebroids. We will show so
me results and examples appearing in a\njoint work with M.Corrêa and A.Mo
linuevo.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giosuè Muratore (UFMG)
DTSTART:20210324T183000Z
DTEND:20210324T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/39
DESCRIPTION:Title: Enumeration of rational contact curves via torus actions\nby Gios
uè Muratore (UFMG) as part of Brazilian algebraic geometry seminar\n\n\nA
bstract\nComplex projective spaces of odd dimension have a unique contact
structure. So\, in these spaces we have contact (Legendrian) rational curv
es. We are interested in enumeration of such curves. We prove that some Gr
omov-Witten numbers associated to rational contact curves in projective sp
ace with arbitrary incidence conditions are enumerative. Also\, we use Bot
t formula on the Kontsevich space to find the exact value of those numbers
.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danny Taboada / Victor Pretti (UFF / UNICAMP)
DTSTART:20210331T183000Z
DTEND:20210331T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/40
DESCRIPTION:Title: The moduli space of quasistable spin curves / Rank 0 Asymptotic Bridg
eland stability\nby Danny Taboada / Victor Pretti (UFF / UNICAMP) as p
art of Brazilian algebraic geometry seminar\n\n\nAbstract\nYoung BRAG\n\nS
peaker 1: Danny Taboada (UFF)\n\nTitle: The moduli space of quasistable sp
in curves\nAbstract: We study a compactification of the moduli space of th
eta characteristics\, giving a modular interpretation of the geometric poi
nts and describing the boundary stratification. This space is different fr
om the moduli space of spin curves. The modular description and the bounda
ry stratification of the new compactification are encoded by a tropical mo
duli space. We show that this tropical moduli space is a refinement of the
moduli space of spin tropical curves. We describe explicitly the induced
decomposition of its cones. This is a joint work with Abreu and Pacini.\n\
n--XX--XX--\n\nSpeaker 2: Victor Pretti (UNICAMP)\n\nTitle: Rank 0 Asympto
tic Bridgeland stability\n\nAbstract: Bridgeland stability is a modern too
l to study stability of objetcs in triangulated categories\, and specially
in the derived category of coherent sheaves over a smooth projective vari
ety. Its asymptotic version\, as studied by Bridgeland\, Bayer and Jardim-
-Maciocia\, is known to behave like Gieseker stability for sheaves in vari
ous situations. In this seminar we will focus on Bridgeland stabilities ov
er the projective space P^3 and its asymptotic behaviour for rank zero obj
ects to prove their respective relation with Gieseker stability for sheave
s.\n\nTwo 30 min presentations by PhD students or recently graduated PhDs.
\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cancelled
DTSTART:20210407T183000Z
DTEND:20210407T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/41
DESCRIPTION:by Cancelled as part of Brazilian algebraic geometry seminar\n
\n\nAbstract\nWith great sadness\, we cancel the BRAG seminar today (07 Ap
ril 2021) due to the passing of our dear friend and colleague Roberto Call
ejas Bedregal\, last night by covid. May he always be remembered for his j
oy\, generosity and good heart\, and may he rest in peace.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aline Andrade (UFF)
DTSTART:20210414T183000Z
DTEND:20210414T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/42
DESCRIPTION:Title: On rank 3 instanton bundles on projective 3 space\nby Aline Andra
de (UFF) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nWe
investigate rank $3$ instanton bundles on $\\mathbb{P}^3$ of charge $n$ a
nd its correspondence with rational curves of degree $n+3$. in order to pr
ove that the generic stable rank 3 ’t Hooft bundle of charge n is a smoo
th point in the moduli space of rank 3 vector bundles of Chern classes (0\
,n\,0). Additionally\, for $n=2$ we present a correspondence between stabl
e rank $3$ instanton bundles and stable rank $2$ reflexive linear sheaves
and we prove that the moduli space of rank $3$ stable locally free sheaves
on $\\mathbb{P}^3$ of Chern classes $(0\,2\,0)$ is irreducible\, generica
lly smooth of dimension 16. (Joint work with D. R. Santiago\, D. D. Silva\
, and L. S. Sobral)\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Ribon (UFF)
DTSTART:20210505T183000Z
DTEND:20210505T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/43
DESCRIPTION:Title: Local foliations with closed leaves\nby Javier Ribon (UFF) as par
t of Brazilian algebraic geometry seminar\n\n\nAbstract\nOur goal is descr
ibing the leaf space of local holomorphic foliation whose leaves are close
d in a neighborhood of the origin. By considering the holonomy groups asso
ciated to leaves\, it is necessary to study the finitely generated groups
of local biholomorphisms whose orbits are closed (or equivalently finite)
in some neighborhood of the origin. We show that for such groups\, there i
s always an analytic curve through the origin that is contained in the fix
ed point set of a finite index subgroup. Moreover\, we outline the propert
ies of the linear part of a local diffeomorphism with finite orbits. The r
esult provides a stability result à la Reeb in intermediate dimension for
dimension one foliations defined in the neighborhood of a compact invaria
nt curve. This is a joint work with Lucivanio Lisboa and some of the resul
ts are part of his PhD thesis.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elizaveta Vishnyakova (UFMG)
DTSTART:20210512T183000Z
DTEND:20210512T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/44
DESCRIPTION:Title: Donagi-Witten construction and a graded covering of a supermanifold\nby Elizaveta Vishnyakova (UFMG) as part of Brazilian algebraic geometr
y seminar\n\n\nAbstract\nIn the paper "Super Atiyah classes and obstructio
ns to splitting of\nsupermoduli space"\, Donagi and Witten suggested a con
struction of a\nfirst obstruction class for splitting of a supermanifold
via\ndifferential operators. We generalize this idea. As a result we\nobta
in a family of embeddings of the category of supermanifolds into\nthe cat
egory of iterated vector bundles and into the category of\ngraded manifol
ds. It was shown that the images of a supermanifold in\nthese categories s
atisfy universal properties of a graded covering or\na graded semicovering
. In our talk we will discuss these functors in the case of a Lie supergro
up and a Lie superalgebra. (Joint work with M. Rotkiewicz).\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Paulo Figueiredo (IMPA)
DTSTART:20210428T183000Z
DTEND:20210428T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/45
DESCRIPTION:Title: Regular foliations on rationally connected threefolds with nef antica
nonical bundle\nby João Paulo Figueiredo (IMPA) as part of Brazilian
algebraic geometry seminar\n\n\nAbstract\nIn his classification of regular
foliations on surfaces\, Brunella showed that every regular foliations on
a rational surface is algebraically integrable\, with rational leaves. Th
is leads to the conjecture\, due to Touzet\, that every regular foliation
on a rationally connected manifold is algebraically integrable with ration
ally connected leaves. This conjecture was shown to be true by Druel for t
he case of Fano manifolds. In this talk\, we will present progress towards
this conjecture for threefolds\, by showing that it is true for regular f
oliations of codimension one on threefolds with nef anticanonical bundle.\
n
LOCATION:https://stable.researchseminars.org/talk/BRAG/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Franco (IST Lisboa)
DTSTART:20210519T183000Z
DTEND:20210519T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/46
DESCRIPTION:Title: Deformation theory for orthogonal and symplectic sheaves\nby Emil
io Franco (IST Lisboa) as part of Brazilian algebraic geometry seminar\n\n
\nAbstract\nModuli spaces of principal bundles usually carry interesting\n
geometric structures\, being a powerful\, and often unique\, source of\nex
amples of varieties with prescribed properties and characteristics.\nNever
theless\, these spaces might be non-compact whenever the base\n(smooth) sc
heme has dimension higher than 1. Principal sheaves provide a\nnatural com
pactification of the moduli space of principal bundles for a\nconnected co
mplex reductive structure group. Therefore\, moduli spaces of\nprincipal s
heaves are projective varieties equipped with an interesting\ngeometry\, a
t least\, on a dense subset. In order to check whether or not\nthese prope
rties extend to the compactification\, we need a local\ndescription of the
moduli spaces\, precisely over the locus where the\nprincipal sheaves fai
l to be principal bundles. Such description would\nnaturally derive from d
eformation theory of principal sheaves\, which is\nstill missing at presen
t date.\n\nIn this talk we consider orthogonal and symplectic sheaves\, an
d show\nthat the deformation and obstruction theory of these objects is\nc
ontrolled by a deformation complex naturally built out of our starting\nor
thogonal (resp. symplectic) sheaf.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeriano Lanza (UFF)
DTSTART:20210526T183000Z
DTEND:20210526T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/47
DESCRIPTION:Title: Moduli of flags of sheaves: a quiver description\nby Valeriano La
nza (UFF) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nI
n [1]\, the moduli spaces of framed flags of sheaves on P2 were described
by means of representations of the so-called enhanced ADHM quiver. We firs
t review those results\, with a recent refinement concerning the chamber s
tructure in the space of stability parameters. We shall then discuss the o
bstruction theory for these moduli spaces\, showing in general that they h
ave a perfect obstruction theory\, and providing for specific choices of
invariants a class of unobstructed points. Finally\, open problems and pos
sible further developments will be presented. This is a joint work with Ro
drigo von Flach and Marcos Jardim. \n\n[1] R. A. von Flach and M. Jardim\,
Moduli spaces of framed flags of sheaves on the projective plane. Journal
of Geometry and Physics 118 (2017)\, 138–168.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Massarenti (U. Ferrara)
DTSTART:20210421T183000Z
DTEND:20210421T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/48
DESCRIPTION:Title: Complete symplectic quadrics and Kontsevich moduli spaces of conics i
n Lagrangian Grassmannians\nby Alex Massarenti (U. Ferrara) as part of
Brazilian algebraic geometry seminar\n\n\nAbstract\nGiven a reductive alg
ebraic group $G$ and a Borel subgroup $B$\, a spherical variety\nis a norm
al variety admitting an action of $G$ with an open dense $B$-orbit. A spec
ial\nclass of spherical varieties are the so-called wonderful varieties. T
hese are smooth\nspherical varieties for which we require $G$ to be semisi
mple and simply connected\nand the existence of an open $B$-orbit whose co
mplementary set is a simple normal\ncrossing divisor. We will construct th
e wonderful compactification of the space of\nsymmetric\, symplectic matri
ces on which the symplectic group acts. Furthermore\,\nwe will compute the
Picard group of this compactification and we will study its\nbirational g
eometry in low-dimensional cases. As an application\, we will recover the\
nresults on the birational geometry of the Kontsevich spaces of conics in
Grassmannians\ndue to I. Coskun and D. Chen\, and we will prove new result
s on the birational\ngeometry of the Kontsevich spaces of conics in Lagran
gian Grassmannians.\nThis is a joint work with Elsa Corniani.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Montoya (UNICAMP)
DTSTART:20210602T183000Z
DTEND:20210602T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/49
DESCRIPTION:Title: An extension of the Noether-Lefschetz loci in toric varieties\nby
William Montoya (UNICAMP) as part of Brazilian algebraic geometry seminar
\n\n\nAbstract\nIn this talk\, I will motivate and prove a Noether-Lefsche
tz type theorem for quasi-smooth intersections in a projective simplicial
toric variety with suitable conditions\, which implies that the Hodge conj
ecture holds on a very general quasi-smooth intersection variety and that
the natural extension of the Noether-Lefchetz loci is not empty. The Noeth
er-Lefschetz loci can be understood as the loci where the Hodge conjecture
is unknown. If time allows me\, I will also show that the Hodge conjectur
e is also true for some varieties in the Noether-Lefschetz loci. This is j
oint work with Prof. Ugo Bruzzo.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abramo Hefez\, Steven Kleiman\, Michelle Morgado\, Marcelo Saia\,
José Seade\, Otoniel Nogueira da Silva
DTSTART:20210609T183000Z
DTEND:20210609T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/50
DESCRIPTION:Title: An afternoon of algebraic geometry in memory of Roberto Bedregal\
nby Abramo Hefez\, Steven Kleiman\, Michelle Morgado\, Marcelo Saia\, Jos
é Seade\, Otoniel Nogueira da Silva as part of Brazilian algebraic geomet
ry seminar\n\n\nAbstract\nwe convene for a special edition of the BRAG (Br
azilian Algebraic Geometry Seminar) session in honor of our friend and col
league Roberto Callejas-Bedregal\, who passed away on 6 April of this year
. We will have 15 minute lectures given by Abramo Hefez (UFF)\, Steven Kle
iman (MIT)\, Michelle Morgado (Unesp)\, Marcelo José Saia (UFSCar)\, Jos
é Seade (UNAM) and Otoniel Nogueira da Silva (UNAM)\, along with testimon
ials from Roberto's students\, friends and colleagues.\n\n-- xx -- xx --\n
\n1 - Abramo Hefez: The mathematical trajectory of Roberto Bedregal Abstra
ct:\nThe aim of this short talk is to sketch Bedregal's journey towards hi
s mathematical achievements.\n\n\n-- xx -- xx --\n\n2 - Steve Kleiman: Rob
erto's MIT Thesis\nTo begin\, some introductory remarks are made about how
Roberto\ncame to study at MIT and to develop the first purely algebraic t
reatment\nof the Whitney Conditions. Then the main result of his thesis i
s\nstated\, and its terms\, explained. Finally\, an inkling is given of t
he\nimport of the Whitney Conditions.\n\n-- xx -- xx --\n\n3 - José Seade
: Chern classes for singular varieties.\nI will speak about some of the jo
int work I did recently with Roberto Callejas-Bedregal and Michelle Morgad
o\, about Chern classes of singular varieties.\n\n-- xx -- xx --\n\n4 - Mi
chelle Morgado: Lê cycles\n\n-- xx -- xx --\n\n5 - Marcelo José Saia: On
Segre numbers of homogeneous map germs\n\n-- xx -- xx --\n\n6 - Otoniel N
ogueira da Silva: Equisingularity of families of map germs and Ruas's Conj
ecture\n\n-- xx -- xx --\n\n7 - Presentation of a video made by Roberto's
students.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaia Comaschi (University of Campinas)
DTSTART:20210616T183000Z
DTEND:20210616T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/51
DESCRIPTION:Title: Instanton sheaves of low charge on Fano threefolds\nby Gaia Comas
chi (University of Campinas) as part of Brazilian algebraic geometry semin
ar\n\n\nAbstract\nLet $X$ be a Fano threefold of Picard number one and of
index $2+h\, \\ h=0\,1$. \nAn \\textit{instanton sheaf of charge $k$ on $X
$} is defined as a semi-stable rank 2 torsion free sheaf $F$ with Chern cl
asses $c_1=-h\, \\ c_2=k\, \\ c_3=0$ and such that $F(-1)$ has no cohomolo
gy.\nLocally free instantons\, originally defined on the projective space
and later generalised on other Fano threefolds $X$\, had been largely stud
ied from several authors in the past years\; their moduli spaces present a
n extremely rich geometry and useful applications to the study of curves o
n $X$.\nIn this talk I will illustrate several features of non-locally fre
e instantons of low charge on 3 dimensional quadrics and cubics. I will fo
cus in particular on the role that they play in the study of the Gieseker-
Maruyama moduli space $M_X(2\;-h\,k\,0)$ and describe how we can still rel
ate these sheaves to curves on $X$.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Jardim (University of Campinas)
DTSTART:20210623T183000Z
DTEND:20210623T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/52
DESCRIPTION:Title: Logarithmic sheaves for complete intersections\nby Marcos Jardim
(University of Campinas) as part of Brazilian algebraic geometry seminar\n
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Letterio Gatto (Politecnico di Torino)
DTSTART:20210630T183000Z
DTEND:20210630T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/53
DESCRIPTION:Title: On the Vertex Operators Representation of Lie Algebras of Matrices\nby Letterio Gatto (Politecnico di Torino) as part of Brazilian algebrai
c geometry seminar\n\n\nAbstract\nRelying on our common skill to multiply
square matrices by vectors\, recalled in the first part of the talk\, we w
ill describe the exterior algebra of a polynomial ring in one indeterminat
e\, and/or the ring of symmetric polynomials\, as a representation of the
Lie algebra of matrices of infinite size with all but finitely many zero e
ntries.\n\nThe description is achieved by bridging classical Schubert calc
ulus on Grassmannians to the vertex operators occurring in the so-called b
oson-fermion correspondence (Poincaré duality for Grassmannians of infini
te dimensional linear spaces) and highlights a substantial generalization
of a classical picture drawn in the Eighties by Date\, Jimbo\, Kashiwara a
nd Miwa\, within the framework of algebraic analysis and infinite dimensio
nal completely integrable systems. The talk will survey joint work with (i
n alphabetical order) O. Behzad\, A. Contiero\, D. Martins\, P. Salehyan\,
I. Scherbak and R. Vidal Martins.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arturo Fernández Pérez (Federal University of Minas Gerais (UFMG
))
DTSTART:20210825T183000Z
DTEND:20210825T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/55
DESCRIPTION:Title: Number of Milnor and Tjurina of Foliations\nby Arturo Fernández
Pérez (Federal University of Minas Gerais (UFMG)) as part of Brazilian al
gebraic geometry seminar\n\n\nAbstract\nIn this talk\, I will show the rel
ationship between the Milnor and Tjurina numbers of a foliation in the com
plex plane. Such numbers are similar to the classic Milnor and Tjurina num
bers for singular curves. This work is in collaboration with Evelia Garcí
a Barroso (Universidad de la Laguna - Spain) and Nancy Saravia Molina (PUC
P-Peru)\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thiago Fassarella (UFF)
DTSTART:20210901T183000Z
DTEND:20210901T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/56
DESCRIPTION:Title: Moduli spaces of parabolic Higgs bundles\nby Thiago Fassarella (U
FF) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nWe are
interested in studying moduli spaces of parabolic Higgs bundles on (punctu
red) curves. A ramified cover between curves defines a map between the cor
responding moduli spaces\, and we will discuss the behavior of this map wi
th respect to the Hitchin fibration. This is joint work in progress with
Frank Loray.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hossein Movasati (IMPA)
DTSTART:20210908T183000Z
DTEND:20210908T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/57
DESCRIPTION:Title: Ibiporanga: A moduli space for differential equations of automorphic
forms\nby Hossein Movasati (IMPA) as part of Brazilian algebraic geome
try seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Salomão (UFF)
DTSTART:20210915T183000Z
DTEND:20210915T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/58
DESCRIPTION:Title: On the classification of fibrations by singular curves on unirational
surfaces\nby Rodrigo Salomão (UFF) as part of Brazilian algebraic ge
ometry seminar\n\n\nAbstract\nIn 1944 Zariski discovered that Bertini’s
theorem on variable singular points is no longer true when we pass from a
field of characteristic zero to a field of positive characteristic. In oth
er words\, he found fibrations by singular curves\, which only exist in po
sitive characteristic. Such fibrations are connected with many interesting
phenomena. For instance\, the extension of Enrique’s classification of
surfaces to positive characteristic (Bombieri and Mumford in 1976)\, the c
ounterexamples of Kodaira vanishing theorem (Mukai in 2013 and Zheng in 20
16) and the isolated singularities with infinity Milnor number (jointly wo
rk with Hefez and Rodrigues in 2019). In this talk we are going to show th
at the smoothing process introduced by Shimada in 1991 can be used to desc
ribe the set of fibrations by genus two singular curves on unirational sur
faces\, up to isomorphism among their generic fibers\, such that the smoot
hing are elliptic fibrations. Moreover we will also describe the vector fi
elds whose tangencies with elliptic fibrations generate such fibrations by
singular curves\, after the quotient of the rational elliptic surfaces. T
his is a work in progress with J. H. O. Rodrigues and R. O. C. Santos.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ommolbanin Behzad / Eduardo Vital (University of Isfahan\, Iran /
IMPA\, Brazil)
DTSTART:20210929T183000Z
DTEND:20210929T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/59
DESCRIPTION:Title: Exterior powers\, Polynomial rings and Representation of Lie Algebras
/ Degenerations of linear series to curves with three components\, using
quiver representations\nby Ommolbanin Behzad / Eduardo Vital (Universi
ty of Isfahan\, Iran / IMPA\, Brazil) as part of Brazilian algebraic geome
try seminar\n\n\nAbstract\nYoung BRAG with two short presentations:\n\nSpe
aker 1: Ommolbanin Behzad (University of Isfahan\, Iran)\n\nTitle: Exterio
r powers\, Polynomial rings and Representation of Lie Algebras\n\nAbstract
: I will report on some recent work of myself\, A. Contiero\, D.\nMartins\
, R. Vidal Martins about representing lie algebras of vector space\nendomo
rphisms on exterior algebras\, seeing it as the finite type case of the\nc
elebrated DJKM bosonic vertex operator representation of gl∞(Q).\n\n\n--
xx -- xx --\n\n\nSpeaker 2: Eduardo Vital (IMPA\, Brazil)\n\nTitle: Degen
erations of linear series to curves with three components\, using quiver r
epresentations\n\nAbstract: We explore the existence of simple bases for c
ertain special quiver representations arising from degenerations of linear
series on nodal curves. The existence\nof a simple basis implies that the
representation decomposes into representations\nof dimension one and simp
lifies the calculus of the Hilbert polynomial of the\nquiver Grassmannian
associated to the representation. For these quiver representations\, we ch
aracterise the existence of a simple basis with a local condition.\nAnd to
a nodal curve with three components we show that its linked projective\ns
pace is Cohen-Macaulay\, reduced\, and has pure dimension.\nThis is a join
t work in progress with Eduardo Esteves and Renan Santos.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Vallès (University of Pau\, France)
DTSTART:20211006T183000Z
DTEND:20211006T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/60
DESCRIPTION:Title: Free curves obtained from a pencil of algebraic curves\nby Jean V
allès (University of Pau\, France) as part of Brazilian algebraic geometr
y seminar\n\n\nAbstract\nAn algebraic curve of the projective plane is fre
e if its module of tangent vectors fields is free\,\nin other words\, if i
t is generated globally by two tangent vector fields.\nBeing given two alg
ebraic curves without common component I propose a new method to produce f
ree curves\n and a theorem explaining why they are free.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacqueline Arancibia (UFPB)
DTSTART:20211027T183000Z
DTEND:20211027T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/61
DESCRIPTION:Title: Some applications of Bott's Localization Formula in Enumerative Probl
ems\nby Jacqueline Arancibia (UFPB) as part of Brazilian algebraic geo
metry seminar\n\n\nAbstract\nFirst of all we explain what are the mathemat
ical objects involved in the Bott's localization formula. Next\, we apply
the Bott's localization formula to resolve the classical problem of four l
ines (from Schubert's Calculus)\, as well as\, to compute the degree of t
he subvariety formed by the surfaces of degree d in ${\\mathbb P}^3$ cont
aining a conic and two points varying on a fixed line.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cleto B. Miranda-Neto (UFPB)
DTSTART:20211103T183000Z
DTEND:20211103T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/62
DESCRIPTION:Title: Vanishing of Ext modules and characterizations of smoothness in algeb
raic varieties\nby Cleto B. Miranda-Neto (UFPB) as part of Brazilian a
lgebraic geometry seminar\n\n\nAbstract\nIn this talk\, after presenting s
ome homological results which establish freeness criteria for modules\, I
will discuss how the vanishing of suitable Ext modules can be translated i
n terms of smoothness of a complex algebraic variety at a given point. Spe
cial attention will be given\, e.g.\, to complete intersections and ration
al surface singularities.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Hassanzadeh (UFRJ)
DTSTART:20211110T183000Z
DTEND:20211110T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/63
DESCRIPTION:Title: A genus explanation of Buchsbaum-Rim multiplicity\nby Hamid Hassa
nzadeh (UFRJ) as part of Brazilian algebraic geometry seminar\n\n\nAbstrac
t\nWe explain the Buchsbaum-Rim multiplicity as the Euler-Poincare charact
eristic of an “ordinary” Koszul complex. This provides a generalizatio
n of Serre’s formula for the Hilbert-Samuel multiplicity in terms of the
length of the Koszul homologies.The talk is based on a joint work with: V
iniçius Bouça\, Thiago Fiel and Jose Naeliton.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristhian Garay (CIMAT\, Guanajuato)
DTSTART:20211117T183000Z
DTEND:20211117T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/64
DESCRIPTION:Title: Inflection polynomials of linear series on superelliptic curves\n
by Cristhian Garay (CIMAT\, Guanajuato) as part of Brazilian algebraic geo
metry seminar\n\n\nAbstract\nWe explore the inflectionary behavior of line
ar series on families of marked superelliptic curves (i.e.\, cyclic covers
of P^1). The inflection of these linear series supported away from the su
perelliptic ramification locus is parameterized by the inflection polynomi
als\, a certain infinite class of polynomials generalizing the division po
lynomials (which are used to compute the torsion points of elliptic curves
).\n\nThese polynomials are remarkable since their properties reflect aspe
cts of the underlying family of superelliptic curves. We also obtain infle
ctionary varieties\, which describe the global behaviour of the inflection
points on the family.\n\nIn this talk we will introduce these inflection
polynomials and some of their properties. We report on joint work with Et
han Cotterill\, Ignacio Darago\, Changho Han\, and Tony Shaska.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarida Melo (Roma Tre University)
DTSTART:20211124T183000Z
DTEND:20211124T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/65
DESCRIPTION:Title: Tropicalization of the universal Jacobian: logarithmic and non-archim
edean viewpoints\nby Margarida Melo (Roma Tre University) as part of B
razilian algebraic geometry seminar\n\n\nAbstract\nWe construct a tropical
universal Jacobian on the category of cone stacks\, generalizing previous
work by Abreu and Pacini. We then show that this cone stack can be obtain
ed by tropicalizing two versions of the algebraic universal Jacobian: the
logarithmic universal Jacobian and the non-archimedean universal Jacobian.
We then discuss the connection between our construction and Molcho-Wise
’s logarithmic Picard and Picard stacks. The talk will be based on joint
work with S. Molcho\, M. Ulirsch\, F. Viviani and J. Wise.\n\nhttps://imp
a-br.zoom.us/j/86824790044?pwd=aDBhcXRVWjR5RXdUeHRhVFdVMzVYUT09\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Esteves (IMPA)
DTSTART:20211201T183000Z
DTEND:20211201T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/66
DESCRIPTION:Title: Degenerations of line bundles and divisors along curves\nby Eduar
do Esteves (IMPA) as part of Brazilian algebraic geometry seminar\n\n\nAbs
tract\nA family of line bundles along a family of smooth curves parameteri
zed by the\npunctured disk can be extended in several ways over the limit
stable curve of the\nfamily. On the other hand\, the associated divisors c
an each be extended in a unique way. We will discuss the interplay between
these two dynamics\, part of an ongoing work to address the problem raise
d by Eisenbud and Harris in the 1980’s of constructing a useful moduli o
f limit linear series over the\nmoduli of stable curves. It involves colla
boration with Piere Rodríguez\, Renan Santos\, Eduardo Vital (IMPA) and O
mid Amini (École Polytechnique).\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato Vidal Martins (UFMG)
DTSTART:20211208T183000Z
DTEND:20211208T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/67
DESCRIPTION:Title: The Gonality of an Integral Curve\nby Renato Vidal Martins (UFMG)
as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nThis talk
introduces gonality for arbitrary integral curves\, and reports\non joint
work in progress with Steve Kleiman. Discussed are topics that\nappear na
turally\, including the following: linear series defined by\ntorsion-free
sheaves of rank 1\; the relation among gonality\, scrolls\,\nand canonical
models\; and an upper bound on gonality.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (Impa)
DTSTART:20230426T173000Z
DTEND:20230426T183000Z
DTSTAMP:20260404T095356Z
UID:BRAG/68
DESCRIPTION:Title: The Calabi Problem for Fano Threefolds\nby Carolina Araujo (Impa)
as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nThe Calabi
Problem is a formidable problem in the confluence of differential and alg
ebraic geometry. It asks which compact complex manifolds admit a Kähler-E
instein metric. A necessary condition for the existence of such a metric i
s that the canonical class of the manifold has a definite sign. For manifo
lds with zero or positive canonical class\, the Calabi problem was solved
by Yau and Aubin/Yau in the 1970s. They confirmed Calabi's prediction\, sh
owing that these manifolds always admit a Kähler-Einstein metric. On the
other hand\, for projective manifolds with negative canonical class\, call
ed “Fano manifolds”\, the problem is much more subtle: Fano manifolds
may or may not admit a Kähler-Einstein metric. The Calabi problem for Fan
o manifolds has attracted much attention in the last decades\, resulting i
n the famous Yau-Tian-Donaldson conjecture. The conjecture\, which is now
a theorem\, states that a Fano manifold admits a Kähler-Einstein metric i
f and only if it satisfies a sophisticated algebro-geometric condition\, c
alled “K-polystability”. In the last few years\, tools from birational
geometry have been used with great success to investigate K-polystability
. In this talk\, I will present an overview of the Calabi problem\, the re
cent connections with birational geometry\, and the current state of the a
rt in dimension 3.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thiago Fassarella (UFF)
DTSTART:20230426T190000Z
DTEND:20230426T200000Z
DTSTAMP:20260404T095356Z
UID:BRAG/69
DESCRIPTION:Title: Torelli-type theorems\nby Thiago Fassarella (UFF) as part of Braz
ilian algebraic geometry seminar\n\n\nAbstract\nIn this talk\, I will pres
ent some Torelli-type theorems concerning moduli spaces of parabolic vecto
r bundles and logarithmic connections over an elliptic curve. In the case
of vector bundles\, we extend a classical theorem of D. Mumford and P. New
stead to the parabolic context (joint work with Luana Justo). For connecti
ons\, we recover the spectral data from the symplectic structure of the mo
duli space (joint work with Frank Loray and Alan Muniz).\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Israel Vainsencher (UFMG)
DTSTART:20230629T140000Z
DTEND:20230629T145000Z
DTSTAMP:20260404T095356Z
UID:BRAG/70
DESCRIPTION:Title: Grau de componentes do espaço de folheações em P^3\nby Israel
Vainsencher (UFMG) as part of Brazilian algebraic geometry seminar\n\n\nAb
stract\nRevisitaremos algumas componentes conhecidas\, e.g.\,\n1) $\\{aA d
B-bB dA\, a=\\deg A/mdc\, b=\\deg B/mdc\\}$\; \n2) pullback linear $\\math
bb{P}^3 \\rightarrow \\mathbb{P}^2$\;\n3) pullback linear $\\mathbb{P}^3 \
\rightarrow \\mathbb{P}^1 \\times \\mathbb{P}^1$.\nO primeiro caso tem gra
u conhecido apenas se $a|b$ ou se $a=2$ e $b$ é ímpar. O segundo caso ad
mite uma fórmula explícita. Por fim\, explicaremos trabalho em andamento
com Vivi Ferrer sobre o grau de componentes descobertas recentemente por
Wodson Mendson.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mauricio Corrêa (U. Bari)
DTSTART:20230629T150000Z
DTEND:20230629T155000Z
DTSTAMP:20260404T095356Z
UID:BRAG/71
DESCRIPTION:Title: Enumerative geometry of Legendrian foliations: a tale of contact\
nby Mauricio Corrêa (U. Bari) as part of Brazilian algebraic geometry sem
inar\n\n\nAbstract\nA foliation by curves is called Legendrian if it is ta
ngent to some distribution of contact on a projective 3-space. Our goal is
to give formulas for the dimensions and degrees of the varieties of Legen
drian foliations\, and of the varieties of foliations tangent to a pencil
of planes which are in terms of Athus polynomial. This is a joint work wit
h Israel Vainsencher.\n
LOCATION:https://stable.researchseminars.org/talk/BRAG/71/
END:VEVENT
END:VCALENDAR