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ON THE CHOW RING OF CERTAIN LEHN–LEHN–SORGER–VAN STRATEN EIGHTFOLDS

Part of: Cycles and subschemes

Published online by Cambridge University Press:  22 March 2021

CHIARA CAMERE ,
ALBERTO CATTANEO  and
ROBERT LATERVEER
CHIARA CAMERE
Affiliation:
Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano (MI), Italy e-mail: chiara.camere@unimi.it
ALBERTO CATTANEO
Affiliation:
Mathematisches Institut and Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany e-mail: cattaneo@math.uni-bonn.de
ROBERT LATERVEER
Affiliation:
Institut de Recherche Mathématique Avancée, CNRS – Université de Strasbourg, 7 Rue René Descartes, 67084 Strasbourg CEDEX, France e-mail: robert.laterveer@math.unistra.fr
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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.

MSC classification

Primary: 14C15: (Equivariant) Chow groups and rings; motives
Secondary: 14C25: Algebraic cycles 14C30: Transcendental methods, Hodge theory , Hodge conjecture
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 2 , May 2022 , pp. 253 - 276
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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