On the Chow groups of some hyperkähler fourfolds with a non-symplectic involution

Abstract

This note concerns hyperkähler fourfolds $X$ having a non-symplectic involution $\iota$. The Bloch-Beilinson conjectures predict the way $\iota$ should act on certain pieces of the Chow groups of $X$. The main result is a verification of this prediction for Fano varieties of lines on certain cubic fourfolds. This has consequences for the Chow ring of the quotient $X/\iota$.

To appear in International Journal of Math., 18 pages, comments welcome ! arXiv admin note: text overlap with arXiv:1703.03990

References in corpus (3)

• Chow rings and decomposition theorems for families of K3 surfaces and Calabi-Yau hypersurfaces
• Antisymplectic involutions of holomorphic symplectic manifolds
• Symplectic involutions of holomorphic symplectic fourfolds