BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yulieth Prieto Montanez (ICTP) DTSTART:20221109T150000Z DTEND:20221109T170000Z DTSTAMP:20260404T110823Z UID:AlgebraicGeom/1 DESCRIPTION:Title: Alebraic Geometry seminar\nby Yulieth Prieto Montanez (IC TP) as part of ICTP Algebraic Geometry Seminar\n\n\nAbstract\nI: On the ge ometry of hyperkähler manifolds\n\nCompact hyperkähler (HK) manifolds (a lso known as Irreducible holomorphic symplectic manifolds) are higher-dime nsional analogs of K3 surfaces generalising many of their properties. Howe ver\, one of the most valuable theorems\, the Torelli theorem for K3 surfa ces\, is slightly different from the case of HK manifolds. In this part\, we introduce some of the main facts about HK manifolds\, the known example s\, and the notion of deformation type\, which is crucial in order to cons truct new examples of such varieties. In particular\, we focus on the modu li space of stable sheaves of K3 surfaces\, which is an example introduced in the seminal works by Mukai and later continued by Göttsche-Huybrechts \, O'Grady\, and Yoshioka.\n\nII: The birational geometry of hyperkähler manifolds of K3-n type admitting symplectic actions\n\nIn this second part \, we study a particular type of deformation of HK manifolds admitting a s pecial property: they carry a non-trivial symplectic birational map. We wi ll see that using some standard facts in lattice theory\, such varieties a re birational to the moduli space of stable sheaves on K3 surfaces. Furthe rmore\, by applying techniques in a setting of Bridgeland stability condit ions\, we can prove that they are isomorphic to some moduli spaces. This l ast part motivated us to study the wall-crossing of such moduli spaces in order to characterize their Mukai vectors. This is a work in collaboration with D. Mattei and Y. Dutta.\n\nRegister in advance for this meeting:\n\n https://zoom.us/meeting/register/tJYpcOyuqjovGtairkDg-0xtWjPdhgFEQMwz\nAft er registering\, you will receive a confirmation email containing \ninform ation about joining the meeting.\n LOCATION:https://stable.researchseminars.org/talk/AlgebraicGeom/1/ END:VEVENT END:VCALENDAR