One-cycles on Gushel-Mukai fourfolds and the Beauville-Voisin filtration

TL;DR

This paper studies special geometric structures on Gushel-Mukai fourfolds, introduces a new filtration on their Chow group, and verifies a sheaf-cycle correspondence for certain rational curves, advancing understanding of their algebraic cycles.

Contribution

It establishes a new filtration on the Chow group of Gushel-Mukai fourfolds and verifies a sheaf-cycle correspondence for low degree rational curves.

Findings

Invariant locus of the involution is a constant surface

Introduces a filtration on CH_1 of a Gushel-Mukai fourfold

Verifies sheaf/cycle correspondence for low degree rational curves

Abstract

We prove that the invariant locus of the involution associated to a general double EPW sextic is a constant surface and introduce a filtration on $\CH_1$ of a Gushel-Mukai fourfold. We verify the sheaf/cycle correspondence for sheaves supported on low degree rational curves, parallel to the cubic fourfolds case.