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

## TL;DR

This paper verifies predictions about how a non-symplectic involution acts on the Chow groups of certain hyperk"ahler fourfolds, specifically Fano varieties of lines on cubic fourfolds, impacting their Chow rings.

## Contribution

It confirms the Bloch-Beilinson conjecture predictions for specific hyperk"ahler fourfolds with non-symplectic involutions, providing new insights into their Chow groups.

## Key findings

- Verification of Bloch-Beilinson conjecture predictions for specific hyperk"ahler fourfolds
- Analysis of the action of involution on Chow groups
- Implications for the Chow ring of the quotient variety

## 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 $X/\iota$.