On the Chow ring of some special Calabi-Yau varieties

2021/05/10 by Robert Laterveer, Laterveer, Robert
Mathematics · #14C15 #14C25 #14C30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2105.04155

openalex publication_date 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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