Fatighenti and Mongardi have defined Fano varieties of type S6 as zero loci of a certain vector bundle on the Grassmannian $\hbox{Gr}(2,10)$. These varieties have 3 Hodge structures of K3 type in their cohomology. We show that the Chow ring of these varieties also displays "K3 type" behaviour.

中文翻译：

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在 S2 型 Fano 品种的 Chow 环上

Fatighenti 和 Mongardi 将 S6 型的 Fano 变体定义为 Grassmannian $\hbox{Gr}(2,10)$ 上某个向量丛的零位点。这些品种的上同调具有 3 个 K3 型 Hodge 结构。我们表明这些品种的 Chow 环也表现出“K3 型”行为。