Algebraic cycles and Gushel-Mukai fivefolds

TL;DR

This paper proves that Gushel-Mukai fivefolds have a special type of Chow-K"unneth decomposition, leading to injectivity results for certain subrings of their Chow rings into cohomology.

Contribution

It establishes the existence of a multiplicative Chow-K"unneth decomposition for Gushel-Mukai fivefolds, a new result in algebraic geometry.

Findings

Gushel-Mukai fivefolds admit a multiplicative Chow-K"unneth decomposition

A tautological subring of their Chow ring injects into cohomology

Advances understanding of algebraic cycles on these varieties

Abstract

We show that Gushel-Mukai fivefolds admit a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the Chow ring of powers of these varieties injects into cohomology.