CMSA Mathematical Physics Seminar: On product identities and the Chow rings of holomorphic symplectic varieties


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February 3, 2020 12:00 pm - 1:00 pm
CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138

Ignacio Barros - Northeastern University

For a moduli space $M$ of stable sheaves over a K3 surface $X$, we propose a series of conjectural identities in the Chow rings $CH_\star (M \times X^\ell),\, \ell \geq 1,$ generalizing the classic Beauville--Voisin identity for a K3 surface. We emphasize consequences of the conjecture for the structure of the tautological subring $R_\star (M) \subset CH_\star (M).$ We prove the proposed identities when $M$ is the Hilbert scheme of points on a K3 surface. This is based on joint work with L. Flapan, A. Marian and R. Silversmith.