The Chow ring of hyperkähler varieties of $$K3^{[2]}$$-type via Lefschetz actions

Autor: Andreas Kretschmer
Rok vydání: 2021
Předmět:
Zdroj: Mathematische Zeitschrift. 300:2069-2090
ISSN: 1432-1823
0025-5874
Popis: We propose an explicit conjectural lift of the Neron–Severi Lie algebra of a hyperkähler variety X of $$K3^{[2]}$$ K 3 [ 2 ] -type to the Chow ring of correspondences $$\mathrm{CH}^*(X \times X)$$ CH ∗ ( X × 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 cohomological grading operator.
Databáze: OpenAIRE
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