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SUMMARY:Yulieth Prieto Montanez (ICTP)
DTSTART:20221109T150000Z
DTEND:20221109T170000Z
DTSTAMP:20260422T225719Z
UID:AlgebraicGeom/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AlgebraicGeo
 m/1/">Alebraic Geometry seminar</a>\nby Yulieth Prieto Montanez (ICTP) as 
 part of ICTP Algebraic Geometry Seminar\n\n\nAbstract\nI: On the geometry 
 of hyperkähler manifolds\n\nCompact hyperkähler (HK) manifolds (also kno
 wn as Irreducible holomorphic symplectic manifolds) are higher-dimensional
  analogs of K3 surfaces generalising many of their properties. However\, o
 ne of the most valuable theorems\, the Torelli theorem for K3 surfaces\, i
 s slightly different from the case of HK manifolds. In this part\, we intr
 oduce some of the main facts about HK manifolds\, the known examples\, and
  the notion of deformation type\, which is crucial in order to construct n
 ew examples of such varieties. In particular\, we focus on the moduli spac
 e of stable sheaves of K3 surfaces\, which is an example introduced in the
  seminal works by Mukai and later continued by Göttsche-Huybrechts\, O'Gr
 ady\, and Yoshioka.\n\nII: The birational geometry of hyperkähler manifol
 ds of K3-n type admitting symplectic actions\n\nIn this second part\, we s
 tudy a particular type of deformation of HK manifolds admitting a special 
 property: they carry a non-trivial symplectic birational map. We will see 
 that using some standard facts in lattice theory\, such varieties are bira
 tional to the moduli space of stable sheaves on K3 surfaces. Furthermore\,
  by applying techniques in a setting of Bridgeland stability conditions\, 
 we can prove that they are isomorphic to some moduli spaces. This last par
 t motivated us to study the wall-crossing of such moduli spaces in order t
 o characterize their Mukai vectors. This is a work in collaboration with D
 . Mattei and Y. Dutta.\n\nRegister in advance for this meeting:\n\nhttps:/
 /zoom.us/meeting/register/tJYpcOyuqjovGtairkDg-0xtWjPdhgFEQMwz\nAfter regi
 stering\, you will receive a confirmation email containing \ninformation a
 bout joining the meeting.\n
LOCATION:https://researchseminars.org/talk/AlgebraicGeom/1/
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