On the Chow groups of some hyperkähler fourfolds with a non-symplectic involution

Abstract

This paper concerns hyperkähler fourfolds [Formula: see text] having a non-symplectic involution [Formula: see text]. The Bloch–Beilinson conjectures predict the way [Formula: see text] should act on certain pieces of the Chow groups of [Formula: see text]. The main result is a verification of this prediction for Fano varieties of lines on certain cubic fourfolds. This has consequences for the Chow ring of the quotient [Formula: see text].