We consider the Pfaffian–Grassmannian equivalence from the motivic point of view. The main result is that under certain numerical conditions, both sides of the equivalence are related on the level of Chow motives. The consequences include a verification of Orlov's conjecture for Borisov's Calabi–Yau threefolds, and verifications of Kimura's finite-dimensionality conjecture, Voevodsky's smash conjecture and the Hodge conjecture for certain linear sections of Grassmannians. We also obtain new examples of Fano varieties with infinite-dimensional Griffiths group.

中文翻译：

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动机和 Pfaffian-Grassmannian 等价

我们从动机的角度考虑 Pfaffian-Grassmannian 等价性。主要结果是在一定的数值​​条件下，等价的双方在周动机水平上是相关的。结果包括对鲍里索夫卡拉比-丘三重的奥尔洛夫猜想的验证，以及对木村有限维猜想、沃沃茨基的粉碎猜想和格拉斯曼的某些线性部分的霍奇猜想的验证。我们还获得了具有无限维格里菲斯群的 Fano 变体的新例子。