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

Sunday, 30 December, 2018

Published in: 

arXiv:1812.11554

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.

Author(s): 

Chiara Camere
Alberto Cattaneo
Robert Laterveer