Seminar

Geometry Seminar

Stability conditions in families

Speaker:  Martí Lahoz (Universitat de Barcelona)
Date:  Wednesday, 12 May 2021 - 14:00
Place:  Online - zoom.us/j/2203382215

Abstract:
In this talk, I will present a new construction of families of polarized hyperkähler manifolds associated to families of cubic fourfolds. The construction is based on technical progress in the theory of Bridgeland stability conditions on derived categories of algebraic varieties. More specifically, we develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties, as well as a version of that for families of Kuznetsov subcategories, that can be thought as non-commutative varieties. Since the derived category of a cubic fourfold has an associated non-commutative K3 surface, this allows us to generalize the powerful Mukai’s theory for moduli spaces of stable sheaves on K3 surfaces to the setting of cubic fourfolds. This is joint work with A. Bayer, E. Macrì, H. Nuer, A. Perry, and P. Stellari.