On the Chow ring of Fano varieties of type $S2$

TL;DR

This paper proves that specific Fano eightfolds have a Chow ring structure similar to K3 surfaces, using a multiplicative Chow-K"unneth decomposition, advancing understanding of their algebraic cycles.

Contribution

It demonstrates that certain Fano eightfolds possess a multiplicative Chow-K"unneth decomposition, linking their Chow ring structure to that of K3 surfaces, which is a novel result.

Findings

Fano eightfolds have a multiplicative Chow-K"unneth decomposition.

Chow ring of these eightfolds behaves like that of K3 surfaces.

Provides new insights into algebraic cycles of Fano varieties.

Abstract

We show that certain Fano eightfolds (obtained as hyperplane sections of an orthogonal Grassmannian, and studied by Ito-Miura-Okawa-Ueda and by Fatighenti-Mongardi) have a multiplicative Chow-K\"unneth decomposition. As a corollary, the Chow ring of these eightfolds behaves like that of K3 surfaces.