TRINO - Algebraic Geometry Seminar - Tuesday 18 July, at 16:00 - VENUE: ICTP Luigi Stasi seminar room - Laura PERTUSI

[ICTP Math Section]

TRINO - Algebraic Geometry Seminar on: Non-commutative abelian surfaces 
and generalized Kummer varieties

Tuesday 18 Jul 2023 16:00

VENUE: ICTP Leonardo Building - Luigi Stasi Seminar Room


Speaker: Laura Pertusi (University of Milano)

Abstract: Examples of non-commutative K3 surfaces arise from 
semiorthogonal decompositions of the bounded derived category of certain 
Fano varieties. The most interesting cases are those of cubic fourfolds 
and Gushel-Mukai varieties of even dimension. Using the deep theory of 
families of stability conditions, locally complete families of 
hyperkähler manifolds deformation equivalent to Hilbert schemes of 
points on a K3 surface have been constructed from moduli spaces of 
stable objects in these non-commutative K3 surfaces. On the other hand, 
an explicit description of a locally complete family of hyperkähler 
manifolds deformation equivalent to a generalized Kummer variety is not 
yet available. In this talk we will construct families of 
non-commutative abelian surfaces as equivariant categories 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 manifolds 
of generalized Kummer deformation type. /This is a joint work in 
progress with Arend Bayer, Alex Perry and Xiaolei Zhao./

All interested are welcome to attend/
/

/https://indico.ictp.it/event/10421//
/

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