Algebraic cycles on some special hyperkähler varieties

Abstract

This note contains some examples of hyperkähler varieties $X$ having a group $G$ of non-symplectic automorphisms, and such that the action of $G$ on certain Chow groups of $X$ is as predicted by Bloch's conjecture. The examples range in dimension from $6$ to $132$. For each example, the quotient $Y=X/G$ is a Calabi-Yau variety which has interesting Chow-theoretic properties; in particular, the variety $Y$ satisfies (part of) a strong version of the Beauville-Voisin conjecture.

arXiv comment31 pages, to appear in Rendiconti di Matematica, comments welcome !

References in corpus (3)

• Chow rings and decomposition theorems for families of K3 surfaces and Calabi-Yau hypersurfaces
• Algebraic cycles on a generalized Kummer variety
• Symplectic automorphisms of K3 surfaces of arbitrary order