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