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.

中文翻译：

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K3曲面的点的希尔伯特方案的Chow环上的李代数作用

我们构造了Looijenga–Lunts–Verbitsky Lie代数的Neron–Severi部分对K3曲面上的希尔伯特点方案的Chow环的作用。这样就简化了Maulik和Negut的证明，证明了周期类图是由Beauville猜想的除数类生成的子环上的射影。构造的关键步骤是根据Nakajima算子对Lefschetz对偶的一个明确公式。我们的结果还得出了以中岛算子为依据对希尔伯特方案采取单峰行动的公式。