Double EPW sextics and the Voisin filtration on zero-cycles

TL;DR

This paper explores the relationship between the Chow group of zero-cycles on double EPW sextics, Voisin's filtration, and motives, revealing new connections and applications to Fano varieties with infinite-order automorphisms.

Contribution

It establishes a link between the anti-invariant Chow groups of double EPW sextics and Voisin's filtration, and relates their motives to those of Gushel-Mukai fourfolds, with applications to Fano varieties.

Findings

Relation between anti-invariant Chow groups and Voisin's filtration.

Identification of motives of double EPW sextics with Gushel-Mukai fourfolds.

Application to Fano varieties with infinite-order automorphisms.

Abstract

Let $X$ be a double EPW sextic, and $\iota$ its anti-symplectic involution. We relate the $\iota$-anti-invariant part of the Chow group of zero-cycles of $X$ with Voisin's rational orbit filtration. For a general double EPW sextic $X$, we also relate the anti-invariant part of the Chow motive of $X$ with the motive of a Gushel-Mukai fourfold. As an application, we obtain a similar result for certain Fano varieties of lines in cubics with infinite-order birational automorphisms.