Bloch’s conjecture for certain hyperkähler fourfolds

Abstract

On a hyperkahler fourfold X, Bloch's conjecture predicts that any involution acts trivially on the deepest level of the Bloch-Beilinson filtration on the Chow group of 0-cycles. We prove a version of Bloch's conjecture when X is the Hilbert scheme of 2 points on a generic quartic in P 3 , and the involution is the non-natural, non-symplectic involution on X constructed by Beauville. This has consequences for the Chow groups of certain EPW sextics.