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. - 64:2(2022), pp. 253-276. [10.1017/S0017089521000069]
On the chow ring of certain lehn-lehn-sorger-van straten eightfolds
C. Camere
;A. Cattaneo;
2022
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.File | Dimensione | Formato | |
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