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 of the Chow ring of these varieties.

On the chow ring of certain lehn-lehn-sorger-van straten eightfolds / C. Camere, A. Cattaneo, R. Laterveer. - In: GLASGOW MATHEMATICAL JOURNAL. - ISSN 0017-0895. - (2021). [Epub ahead of print] [10.1017/S0017089521000069]

On the chow ring of certain lehn-lehn-sorger-van straten eightfolds

C. Camere
;
A. Cattaneo;
2021

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 of the Chow ring of these varieties.
Settore MAT/03 - Geometria
22-mar-2021
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/837960
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