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Article Dans Une Revue Glasgow Mathematical Journal Année : 2021

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

Chiara Camere
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Alberto Cattaneo
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Résumé

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.

Dates et versions

hal-02311543 , version 1 (11-10-2019)

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Chiara Camere, Alberto Cattaneo, Robert Laterveer. On the Chow ring of certain Lehn-Lehn-Sorger-van Straten eightfolds. Glasgow Mathematical Journal, In press, ⟨10.1017/S0017089521000069⟩. ⟨hal-02311543⟩
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