Symplectic involutions of K3 surfaces act trivially on CH_0

TL;DR

This paper proves that symplectic involutions on K3 surfaces act trivially on the zero-cycle group, confirming a prediction by Bloch's conjecture and extending previous results to all types.

Contribution

It establishes that all symplectic involutions on K3 surfaces act trivially on CH_0, generalizing recent partial results to a complete proof.

Findings

Symplectic involutions act trivially on CH_0 of K3 surfaces.

Confirmed Bloch's conjecture for all symplectic involutions.

Extended previous partial results to a full classification.

Abstract

Symplectic involutions of a K3 surface are those involutions which leave the holomorphic 2-form invariant. We show, as predicted by Bloch's conjecture, that they act trivially on the CH_0 group of the K3 surface. This was recently proved by Huybrechts and Kemeny for one of the three types of symplectic involutions.