Séminaire Géométries ICJ

Derived categories of cubic fourfolds and non-commutative K3 surfaces

Name: Derived categories of cubic fourfolds and non-commutative K3 surfaces
Start: 2019-04-19T10:30:00+02:00
End: 2019-04-19T11:30:00+02:00
Location: ICJ

par Emanuele Macrì

vendredi 19 avr. 2019, 10:30 → 11:30 Europe/Paris

112 (ICJ)

112

ICJ

1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua

Description

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 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.