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Algebraic cycles and Lehn–Lehn–Sorger–van Straten eightfolds

Part of: Cycles and subschemes

Published online by Cambridge University Press:  04 October 2021

Robert Laterveer Open the ORCID record for Robert Laterveer [Opens in a new window]
Robert Laterveer*
Affiliation:
Institut de Recherche Mathématique Avancée, CNRS – Université de Strasbourg, 7 Rue René Descartes, Strasbourg Cedex67084, France(robert.laterveer@math.unistra.fr)
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Abstract

This article is about Lehn–Lehn–Sorger–van Straten eightfolds $Z$ and their anti-symplectic involution $\iota$. When $Z$ is birational to the Hilbert scheme of points on a K3 surface, we give an explicit formula for the action of $\iota$ on the Chow group of $0$-cycles of $Z$. The formula is in agreement with the Bloch–Beilinson conjectures and has some non-trivial consequences for the Chow ring of the quotient.

Keywords

Algebraic cycleschow groupmotiveBloch–Beilinson filtrationBeauville's ‘splitting property’ conjecturemultiplicative Chow–Künneth decompositionhyperkähler varietiesHilbert schemes of K3 surfacesLehn–Lehn–Sorger–van Straten eightfoldsnon-symplectic automorphism

MSC classification

Primary: 14C15: (Equivariant) Chow groups and rings; motives
Secondary: 14C25: Algebraic cycles 14C30: Transcendental methods, Hodge theory , Hodge conjecture

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 4 , November 2021 , pp. 884 - 907
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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