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

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-Künneth decomposition. As a corollary, the Chow ring of these eightfolds behaves like that of K3 surfaces.

arXiv comment11 pages, to appear (in slightly different from) in Abhandlungen Mat. Sem. Univ. Hamburg, comments welcome !