# The Beauville-Voisin conjecture for $\mathsf{Hilb}(K3)$ and the Virasoro algebra – Andrei Negut (MIT)

#### Venue

Dipartimento di Matematica, Aula Magna.

#### Abstract

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.

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