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arXiv · 2010.13847

The Chow ring of hyperk\"ahler varieties of $K3^{[2]}$-type via Lefschetz actions

Andreas Kretschmer
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Abstract

We propose an explicit conjectural lift of the Neron-Severi Lie algebra of a hyperk\"ahler variety $X$ of $K3^{[2]}$-type to the Chow ring of correspondences ${\rm CH}^\ast(X \times X)$ in terms of a canonical lift of the Beauville-Bogomolov class obtained by Markman. We give evidence for this conjecture in the case of the Hilbert scheme of two points of a $K3$ surface and in the case of the Fano variety of lines of a very general cubic fourfold. Moreover, we show that the Fourier decomposition of the Chow ring of $X$ of Shen and Vial agrees with the eigenspace decomposition of a canonical lift of the grading operator.

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Andreas Kretschmer. 2020-10-26. The Chow ring of hyperk\"ahler varieties of $K3^{[2]}$-type via Lefschetz actions. https://arxiv.org/abs/2010.13847

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