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Algebra and Geometry Seminar

Monday, January 29, 2018
4:00pm to 5:00pm
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Building 15, Room 104
K3 categories, cubic 4-folds, and the Beauville-Voisin conjecture
Junliang Shen, Departement Mathematik, ETH Zurich,

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.

For more information, please contact Mathematics Dept. by phone at 626-395-4335 or by email at [email protected].