Algebraic cycles on a very special EPW sextic

TL;DR

This paper investigates algebraic cycles on a special EPW sextic, proving parts of a conjecture related to Chow rings and exploring the structure of Chow groups for these complex geometric objects.

Contribution

It proves a portion of the Chow ring conjecture for a specific EPW sextic and analyzes the Chow groups of related hyperkähler fourfolds.

Findings

Partial proof of the Chow ring conjecture for the special EPW sextic

Results on the structure of Chow groups of related hyperkähler fourfolds

Insights into algebraic cycles on complex hyperkähler varieties

Abstract

Motivated by the Beauville-Voisin conjecture about Chow rings of powers of $K3$ surfaces, we consider a similar conjecture for Chow rings of powers of EPW sextics. We prove part of this conjecture for the very special EPW sextic studied by Donten-Bury et alii. We also prove some other results concerning the Chow groups of this very special EPW sextic, and of certain related hyperk\"ahler fourfolds.