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arXiv · 1812.11554

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

Chiara Camere·Alberto Cattaneo·Robert Laterveer
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Abstract

We consider a $10$-dimensional family of Lehn-Lehn-Sorger-van Straten hyperk\"ahler 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.

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Chiara Camere, Alberto Cattaneo, Robert Laterveer. 2018-12-30. On the Chow ring of certain Lehn-Lehn-Sorger-van Straten eightfolds. https://arxiv.org/abs/1812.11554

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