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SUMMARY:Xiaolei Zhao (University of California\, Santa Barbara)
DTSTART:20251203T080000Z
DTEND:20251203T093000Z
DTSTAMP:20260422T161058Z
UID:HKUST-AG/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HKUST-AG/83/
 ">Non-commutative abelian surfaces and Kummer type hyperkähler manifolds<
 /a>\nby Xiaolei Zhao (University of California\, Santa Barbara) as part of
  Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 4504 (Lift 2
 5/26).\n\nAbstract\nExamples of non-commutative K3 surfaces arise from sem
 iorthogonal decompositions of the bounded derived category of certain Fano
  varieties. The most interesting cases are those of cubic fourfolds and Gu
 shel-Mukai varieties of even dimension. Using the deep theory of families 
 of stability conditions\, locally complete families of hyperkähler manifo
 lds deformation equivalent to Hilbert schemes of points on a K3 surface ha
 ve been constructed from moduli spaces of stable objects in these non-comm
 utative K3 surfaces. On the other hand\, an explicit description of a loca
 lly complete family of hyperkähler manifolds deformation equivalent to a 
 generalized Kummer variety is not yet available.\n\nIn this talk we will c
 onstruct families of non-commutative abelian surfaces as equivariant categ
 ories of the derived category of K3 surfaces which specialize to Kummer K3
  surfaces. Then we will explain how to induce stability conditions on them
  and produce examples of locally complete families of hyperkähler manifol
 ds of generalized Kummer deformation type. Applications to abelian fourfol
 ds of Weil type will be discussed.\n\nThis is joint work in preparation wi
 th Arend Bayer\, Alex Perry and Laura Pertusi.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/83/
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