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

TL;DR

This paper investigates how non-symplectic involutions affect the Chow groups of hyperkähler fourfolds, verifying predictions for specific Fano varieties and exploring implications for their quotient's Chow ring.

Contribution

It verifies Bloch-Beilinson conjecture predictions for the action of involutions on Chow groups of certain hyperkähler fourfolds, specifically Fano varieties of lines on cubic fourfolds.

Findings

Confirmed conjecture predictions for specific hyperkähler fourfolds.

Analyzed the impact of involutions on the Chow ring structure.

Derived consequences for the Chow ring of quotient varieties.

Abstract

This article is about hyperk\"ahler fourfolds $X$ admitting 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 some interesting consequences for the Chow ring of the quotient $X/\iota$.