An explicit Chow-level lift of the Neron-Severi Looijenga-Lunts-Verbitsky Lie algebra action on Hilbert schemes of K3 surfaces is constructed via Nakajima operators.
Lehn's formula in Chow and Conjectures of Beauville and Voisin
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abstract
The Beauville-Voisin conjecture for a hyperk\"ahler manifold X states that the subring of the Chow ring A^*(X) generated by divisor classes and Chern characters of the tangent bundle injects into the cohomology ring of X. We prove a weak version of this conjecture when X is the Hilbert scheme of points on a K3 surface, for the subring generated by divisor classes and tautological classes. This in particular implies the weak splitting conjecture of Beauville for these geometries. In the process, we extend Lehn's formula and the Li-Qin-Wang W_{1+infinity} algebra action from cohomology to Chow groups, for the Hilbert scheme of an arbitrary smooth projective surface S
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A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface
An explicit Chow-level lift of the Neron-Severi Looijenga-Lunts-Verbitsky Lie algebra action on Hilbert schemes of K3 surfaces is constructed via Nakajima operators.