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 $X$.

18 pages, to appear in Canadian Math. Bulletin, comments welcome !

References in corpus (1)

• Crepant resolutions of double covers: On the Cynk-Hulek criterion for crepant resolutions of double cover