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

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.

arXiv commentRevised version. A gap in Lemma 4.12 was discovered and corrected by Carl Mazzanti, whose independently authored appendix is included. Also corrected the definition of theta