Derived categories of cubic fourfolds and non-commutative K3 surfaces

Géométrie Algébrique

Salle de séminaires du M3 (3ème étage)
Emanuele Macrì
IHES/Paris Sud
Mardi, 5 Mars, 2019 - 14:00 - 15:00

The derived category of coherent sheaves on a cubic fourfold has a subcategory which can be thought as the derived category of a non-commutative K3 surface. This subcategory was studied recently in the work of Kuznetsov and Addington-Thomas, among others. In this talk, I will present joint work in progress with Bayer, Lahoz, Nuer, Perry, Stellari, on how to construct Bridgeland stability conditions on this subcategory. This proves a conjecture by Huybrechts, and it allows to start developing the moduli theory of semistable objects in these categories, in an analogue way as for the classical Mukai theory for (commutative) K3 surfaces. I will also discuss a few applications of these results.