On the Chow ring of some special Calabi-Yau varieties. (English) Zbl 1487.14017
Summary: 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 \(X\).
MSC:
| 14C15 | (Equivariant) Chow groups and rings; motives |
| 14C25 | Algebraic cycles |
| 14C30 | Transcendental methods, Hodge theory (algebro-geometric aspects) |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
Keywords:
algebraic cycles; Chow group; motive; Bloch-Beilinson filtration; distinguished cycles; section propertyReferences:
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