A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface
G Oberdieck - Commentarii Mathematici Helvetici, 2021 - ems.press
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.
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.
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