On the Chow ring of certain Fano fourfolds

TL;DR

This paper proves that specific Fano fourfolds of K3 type possess a multiplicative Chow-K"unneth decomposition, leading to new insights into their Chow rings and algebraic structure.

Contribution

It establishes the existence of a multiplicative Chow-K"unneth decomposition for certain Fano fourfolds of K3 type, a novel result in algebraic geometry.

Findings

Existence of multiplicative Chow-K"unneth decomposition for these fourfolds

Implications for the structure of their Chow rings

Enhanced understanding of algebraic cycles on Fano fourfolds

Abstract

We prove that certain Fano fourfolds of K3 type constructed by Fatighenti-Mongardi have a multiplicative Chow-K\"unneth decomposition. We present some consequences for the Chow ring of these fourfolds.