Algebra and Geometry Seminar

We discuss recent progress on the connection between 0-cycles of holomorphic symplectic varie​ties and structures of K3 categories. We propose that there exists a sheaf/cycle correspondence ​for any K3 category, which controls the geometry of algebraically coisotropic subvarieties of certain holomor​phic symplectic varieties.

Two concrete cases will be illustrated in details:

(1) the derived categor​y of a K3 surface (joint with Qizheng Yin and Xiaolei Zhao),

(2) Kuznetsov category of a cubic 4-fold (joint with Qizheng Yin).

If time permits, we will also discuss the connection to rational curves in cubic 4-folds.