On the Chow ring of some special Calabi–Yau varieties

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.