Algebraic and Arithmetic Geometry Seminar

The Beauville-Voisin conjecture for $\mathsf{Hilb}(K3)$ and the Virasoro algebra

by Andrei Negut (MIT)

Aula Magna (Dipartimento di Matematica)

Aula Magna

Dipartimento di Matematica


We give a geometric representation theory proof of a mild version of the Beauville-Voisin Conjecture for Hilbert schemes of $K3$ surfaces, namely the injectivity of the cycle map restricted to the subring of Chow generated by tautological classes. Our approach involves lifting formulas of Lehn and Li-Qin-Wang from cohomology to Chow groups, and using them to solve the problem by invoking the irreducibility criteria of Virasoro algebra modules, due to Feigin-Fuchs. Joint work with Davesh Maulik.