Derived categories of cubic fourfolds and non-commutative K3 surfaces

Mardi 18 avril 2017 14:15-15:15 - Emanuele Macri - Northeastern University

Résumé : 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, Stellari and with Lahoz, Nuer, Perry, 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.

Lieu : Bât. 425, salle 117-119

Derived categories of cubic fourfolds and non-commutative K3 surfaces  Version PDF