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On the Chow ring of some special Calabi–Yau varieties

Part of: Cycles and subschemes

Published online by Cambridge University Press:  11 May 2021

Robert Laterveer
Robert Laterveer*
Affiliation:
Institut de Recherche Mathématique Avancée, CNRS – Université de Strasbourg, 7 Rue René Descartes, 67084Strasbourg CEDEX, France
*
e-mail: [email protected]
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Abstract

We consider Calabi–Yau n-folds X arising from certain hyperplane arrangements. Using Fu–Vial’s theory of distinguished cycles for varieties with motive of abelian type, we show that the subring of the Chow ring of X generated by divisors, Chern classes and intersections of subvarieties of positive codimension injects into cohomology. We also prove Voisin’s conjecture for X, and Voevodsky’s smash-nilpotence conjecture for odd-dimensional X.

Keywords

Algebraic cyclesChow groupmotiveBloch–Beilinson filtrationdistinguished cyclessection property

MSC classification

Primary: 14C15: (Equivariant) Chow groups and rings; motives
Secondary: 14C25: Algebraic cycles 14C30: Transcendental methods, Hodge theory , Hodge conjecture
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 2 , June 2022 , pp. 308 - 327
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

Supported by ANR grant ANR-20-CE40-0023.

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