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.

中文翻译：

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在一些特殊的 Calabi-Yau 品种的 Chow 环上

我们考虑由某些超平面排列产生的Calabi-Yau n -folds X。利用Fu-Vial 的阿贝尔型动机簇的判别循环理论，我们证明了由除数、Chern 类和正余维子类型的交集生成的X的Chow 环的子环注入上同调。我们还证明了对X的 Voisin 猜想和对奇维X的 Voevodsky 的粉碎-幂零猜想。