BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ugo Bruzzo (SISSA / UFPB) DTSTART:20210208T130000Z DTEND:20210208T140000Z DTSTAMP:20260404T095454Z UID:Bandoleros-2021/1 DESCRIPTION:Title: Semistable Higgs bundles on elliptic surfaces\nby Ugo B ruzzo (SISSA / UFPB) as part of V Algebraic Geometry Summer Meeting - Band oleros 2021\n\n\nAbstract\nWe analyze Higgs bundles $(V\,\\phi)$ on a clas s of elliptic surfaces $\\pi:X\\to B$\, whose underlying vector bundle $V$ has vertical determinant and is fiberwise semistable. We prove that if th e spectral curve of $V$ is reduced\, then the Higgs field $\\phi$ is verti cal\, while if the bundle $V$ is fiberwise regular with reduced (resp.\, i ntegral) spectral curve\, and if its rank and second Chern number satisfy an inequality involving the genus of $B$ and the degree of the fundamental line bundle of $\\pi$ (resp.\, if the fundamental line bundle is sufficie ntly ample)\, then $\\phi$ is scalar. We apply these results to the proble m of characterizing slope-semistable Higgs bundles with vanishing discrimi nant on the class of elliptic surfaces considered\, in terms of the semist ability of their pull-backs via maps from arbitrary (smooth\, irreducible\ , complete) curves to $X$. Work in collaboration with V. Peragine.\n LOCATION:https://stable.researchseminars.org/talk/Bandoleros-2021/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Xuqiang Qin (UNC) DTSTART:20210208T141500Z DTEND:20210208T151500Z DTSTAMP:20260404T095454Z UID:Bandoleros-2021/2 DESCRIPTION:Title: Compactification of the moduli space of minimal instantons on the Fano threefold $V_4$\nby Xuqiang Qin (UNC) as part of V Algebra ic Geometry Summer Meeting - Bandoleros 2021\n\n\nAbstract\nInstanton bund les were first introduced on $\\mathbb{P}^{3}$ as stable rank $2$ bundles E with $c_1(E)=0$ and ${\\textrm H}^1(E(-2))=0.$ Torsion free generalizati ons and properties of moduli spaces of instanton bundles have been widely studied. Faenzi and Kuznetsov generalized the notion of instanton bundles to other Fano threefolds. In this talk\, we look at semistable sheaves of rank 2 with Chern classes $c_1 = 0\,$ $c_2 = 2$ and $c_3 = 0$ on the Fano threefold $V_4$ of Picard number $1\,$ degree $4$ and index $2.$ We show t hat the moduli space of such sheaves is isomorphic to the moduli space of semistable rank $2\,$ degree $0$ vector bundles on a genus $2$ curve. This provides a smooth compactification of the moduli space of minimal instant on bundles on $V_4.$\n LOCATION:https://stable.researchseminars.org/talk/Bandoleros-2021/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincenzo Antonelli (Politecnico di Torino) DTSTART:20210208T153000Z DTEND:20210208T173000Z DTSTAMP:20260404T095454Z UID:Bandoleros-2021/3 DESCRIPTION:Title: Ulrich bundles on Hirzebruch surfaces\nby Vincenzo Anto nelli (Politecnico di Torino) as part of V Algebraic Geometry Summer Meeti ng - Bandoleros 2021\n\n\nAbstract\nUlrich bundles on a projective variety are vector bundles without intermediate cohomology and with the maximal p ossible numbers of generators. They can be considered as the vector bundle s with the simplest possible cohomology. \\\\ In this talk we characterize Ulrich bundles of any rank on polarized rational ruled surfaces over $\\m athbb{P}^1$. We show that every Ulrich bundle admits a resolution in terms of line bundles. Conversely\, given an injective map between suitable tot ally decomposed vector bundles\, we show that its cokernel is Ulrich if it satisfies a vanishing in cohomology. Then we deal with the admissible ran ks and first Chern classes of an Ulrich bundle and we present some results about the moduli space of stable Ulrich bundles.\n LOCATION:https://stable.researchseminars.org/talk/Bandoleros-2021/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Faenzi (Université de Bourgogne) DTSTART:20210210T130000Z DTEND:20210210T140000Z DTSTAMP:20260404T095454Z UID:Bandoleros-2021/4 DESCRIPTION:Title: Ulrich bundles on cubic fourfolds\nby Daniele Faenzi (U niversité de Bourgogne) as part of V Algebraic Geometry Summer Meeting - Bandoleros 2021\n\n\nAbstract\nI will report on joint work with Yeongrak K im. Ulrich bundles on an $n-$dimensional closed subscheme $X$ of $\\mathbb {P}^{N}$ are defined as sheaves whose associated module of global sections has a free linear resolution of $N-n$ steps. I will prove that any smooth cubic fourfold $X$ carries an Ulrich sheaf of rank 6. This is the minimal possible rank of an Ulrich sheaf when the fourfold is very general.\n LOCATION:https://stable.researchseminars.org/talk/Bandoleros-2021/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Gianfranco Casnati (Politecnico di Torino) DTSTART:20210210T141500Z DTEND:20210210T151500Z DTSTAMP:20260404T095454Z UID:Bandoleros-2021/5 DESCRIPTION:Title: Ulrich bundles on some regular surfaces\nby Gianfranco Casnati (Politecnico di Torino) as part of V Algebraic Geometry Summer Mee ting - Bandoleros 2021\n\n\nAbstract\nAn Ulrich bundle on a variety X insi de the projective N-space $\\mathbb{P}^{N}$ over the complex field is a ve ctor bundle that admits a linear minimal free resolution as a sheaf on $\\ mathbb{P}^{N}$. Ulrich bundles have many interesting properties. E.g. they are semistable and have no intermediate cohomology: moreover\, their exis tence on a hypersurface $X$ is related to the problem of expressing a powe r of the polynomial defining $X$ as a linear determinant. Ulrich bundles o n complex curves can be easily described. This is no longer true for Ulric h bundles on surfaces\, though an almost easy characterization is still po ssible. In the talk we focus our attention on the latter case. In particul ar we study the case of surfaces $S$ with $q(S):=h^1(O_S)=0$ satisfying so me further technical restriction\, showing the existence of simple Ulrich bundles of rank 2 on them. We also deal with examples for all the admissi ble values of the Kodaira dimension of $S$.\n LOCATION:https://stable.researchseminars.org/talk/Bandoleros-2021/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Fatemeh Rezaee (Loughborough University) DTSTART:20210210T153000Z DTEND:20210210T173000Z DTSTAMP:20260404T095454Z UID:Bandoleros-2021/6 DESCRIPTION:Title: Birational behaviour of sheaves on threefolds\nby Fatem eh Rezaee (Loughborough University) as part of V Algebraic Geometry Summer Meeting - Bandoleros 2021\n\n\nAbstract\nI will describe a new wall-cross ing phenomenon of sheaves on the projective 3-space that induces singulari ties which are not allowed in the sense of the Minimal Model Program. Ther efore\, it cannot be detected as an operation in the Minimal Model Program of the moduli space\, unlike the case for many surfaces.\n LOCATION:https://stable.researchseminars.org/talk/Bandoleros-2021/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander S. Tikhomirov (Higher School of Economics\, Moscow) DTSTART:20210212T130000Z DTEND:20210212T140000Z DTSTAMP:20260404T095454Z UID:Bandoleros-2021/7 DESCRIPTION:Title: Construction of symplectic vector bundles on projective sp ace $\\mathbb{P}^3$\nby Alexander S. Tikhomirov (Higher School of Econ omics\, Moscow) as part of V Algebraic Geometry Summer Meeting - Bandolero s 2021\n\n\nAbstract\nThe moduli spaces of symplectic vector bundles of ar bitrary rank on projective space $\\mathbb{P}^3$ are far from being well-u nderstood. By now the only type of such bundles having satisfactory descri ption are the so-called tame symplectic instantons. It is shown by U. Bruz zo\, D. Markushevich and the author in two papers from 2012 and 2016 that the moduli spaces of tame symplectic instantons are irreducible genericall y reduced algebraic spaces of dimension prescribed by the deformation theo ry. In the present paper we construct an infinite series of smooth irreduc ible moduli components of symplectic vector bundles of an arbitrary even r ank $2r\,r\\ge1$\, obtained by an iterative use of the monad construction applied to tame symplectic instantons. As a particular case we obtain an i nfinite series of irreducible moduli components of stable rank 2 vector bu ndles on $\\mathbb{P}^3$. We show that this series contains as a subseries a large part of an infinite series of moduli components constructed by th e author\, S. Tikhomirov and D. Vassiliev in 2019. We also prove that\, fo r any integers $n\,r$\, where $r\\ge1$ and $n\\ge r+147$\, there exists a moduli component\, not necessarily unique\, of our series such that symple ctic bundles from this component have rank $2r$ and second Chern class $n$ .\n LOCATION:https://stable.researchseminars.org/talk/Bandoleros-2021/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Aline V. Andrade (UFF) DTSTART:20210212T141500Z DTEND:20210212T151500Z DTSTAMP:20260404T095454Z UID:Bandoleros-2021/8 DESCRIPTION:Title: On rank 3 instanton bundles on projective 3 space\nby A line V. Andrade (UFF) as part of V Algebraic Geometry Summer Meeting - Ban doleros 2021\n\n\nAbstract\nWe investigate rank $3$ instanton bundles on $ \\mathbb{P}^3$ of charge $n$ and its correspondence with rational curves o f degree $n+3$. in order to prove that the generic stable rank 3 ’t Hoof t bundle of charge n is a smooth point in the moduli space of rank 3 vecto r bundles of Chern classes (0\,n\,0). Additionally\, for $n=2$ we present a correspondence between stable 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\, generically smooth of dimension 16. (Joint work with D. R. Santiago\, D. D. Silva\, and L. S. Sobral)\n LOCATION:https://stable.researchseminars.org/talk/Bandoleros-2021/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Ricolfi (SISSA) DTSTART:20210212T153000Z DTEND:20210212T173000Z DTSTAMP:20260404T095454Z UID:Bandoleros-2021/9 DESCRIPTION:Title: Virtual invariants of Quot schemes on 3-folds\nby Andre a Ricolfi (SISSA) as part of V Algebraic Geometry Summer Meeting - Bandole ros 2021\n\n\nAbstract\nLet $n > 0$ be an integer. The Quot scheme of leng th $n$ quotients of the free sheaf $\\mathcal{O}^r$ on affine space $\\mat hbb{A}^3$ is the main character in “rank $r$ Donaldson-Thomas theory”. We will explain how to attach several types of invariants (enumerative\, cohomological\, $K-$theoretic\, motivic) to this Quot scheme\, and show th at the resulting generating functions (varying n) have nice plethystic exp ressions. In particular\, the $K-$theoretic formula completely solves the higher rank DT theory of $\\mathbb{A}^3$\, confirming the Awata-Kanno Conj ecture in String Theory. This part is joint work with Nadir Fasola and Ser gej Monavari.\n LOCATION:https://stable.researchseminars.org/talk/Bandoleros-2021/9/ END:VEVENT END:VCALENDAR