# A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface

### Georg Oberdieck

Universität Bonn, Germany

## Abstract

We construct an action of the Neron–Severi part of the Looijenga–Lunts–Verbitsky Lie algebra on the Chow ring of the Hilbert scheme of points on a K3 surface. This yields a simplification of Maulik and Negut’s proof that the cycle class map is injective on the subring generated by divisor classes as conjectured by Beauville. The key step in the construction is an explicit formula for Lefschetz duals in terms of Nakajima operators. Our results also lead to a formula for the monodromy action on Hilbert schemes in terms of Nakajima operators.

## Cite this article

Georg Oberdieck, A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface. Comment. Math. Helv. 96 (2021), no. 1, pp. 65–77

DOI 10.4171/CMH/507