The Chow ring of double EPW sextics

TL;DR

This paper verifies Beauville and Voisin's conjecture for a very general double EPW sextic, showing that polynomial relations between divisor classes and Chern classes hold in Chow groups.

Contribution

It provides the first verification of the conjecture for double EPW sextics, expanding understanding of algebraic cycles on irreducible symplectic varieties.

Findings

Conjecture verified for very general double EPW sextics

Polynomial relations in cohomology hold in Chow groups for these varieties

Supports broader conjectures about algebraic cycles on symplectic varieties

Abstract

A conjecture of Beauville and Voisin states that for an irreducible symplectic variety X, any polynomial relation between classes of divisors and the Chern classes of X which holds in cohomology already holds in the Chow groups. We verify the conjecture for a very general double EPW sextic.