On the Chow ring of certain Lehn-Lehn-Sorger-van Straten eightfolds

Abstract

We consider a $10$-dimensional family of Lehn-Lehn-Sorger-van Straten hyperkähler eightfolds which have a non-symplectic automorphism of order $3$. Using the theory of finite-dimensional motives, we show that the action of this automorphism on the Chow group of $0$-cycles is as predicted by the Bloch-Beilinson conjectures. We prove a similar statement for the anti-symplectic involution on varieties in this family. This has interesting consequences for the intersection product in the Chow ring of these varieties.

Revised version following referee report, to appear in Glasgow Math. J