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

2020/10/26 by A. Kretschmer, Kretschmer, Andreas
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2010.13847

openalex publication_date 2020/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an explicit conjectural lift of the Neron-Severi Lie algebra of a\nhyperk "ahler variety X of K3^[2]-type to the Chow ring of\ncorrespondences rm CH^\∗(X \× X) in terms of a canonical lift of the\nBeauville-Bogomolov class obtained by Markman. We give evidence for this\nconjecture in the case of the Hilbert scheme of two points of a K3 surface\nand in the case of the Fano variety of lines of a very general cubic fourfold.\nMoreover, we show that the Fourier decomposition of the Chow ring of X of\nShen and Vial agrees with the eigenspace decomposition of a canonical lift of\nthe grading operator.\n

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