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On the Chow ring of some special Calabi–Yau varieties

Published online by Cambridge University Press:  11 May 2021

Robert Laterveer*
Affiliation:
Institut de Recherche Mathématique Avancée, CNRS – Université de Strasbourg, 7 Rue René Descartes, 67084Strasbourg CEDEX, France

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.

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Article
Copyright
© Canadian Mathematical Society 2021

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Footnotes

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

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