# On the Chow groups of some hyperk\"ahler fourfolds with a non-symplectic involution

Research paper by Robert Laterveer

Indexed on: 24 Mar '17Published on: 24 Mar '17Published in: arXiv - Mathematics - Algebraic Geometry

#### Abstract

This note concerns hyperk\"ahler 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 $X/\iota$.