On the Chow groups of certain EPW sextics

Abstract

This note is about the Hilbert square X = S^[2], where S is a general K3 surface of degree 10, and the anti-symplectic birational involution ι of X constructed by O'Grady. The main result is that the action of ι on certain pieces of the Chow groups of X is as expected by Bloch's conjecture. Since X is birational to a double EPW sextic X′, this has consequences for the Chow ring of the EPW sextic Y ⊂ P⁵ associated to X′.