On the cohomology of Gushel-Mukai sixfolds

TL;DR

This paper constructs a stable rationality for certain Gushel-Mukai sixfolds and computes their integral singular cohomology, demonstrating that these varieties have torsion-free cohomology groups.

Contribution

It provides the first explicit stable rationality construction for smooth Gushel-Mukai sixfolds and calculates their integral cohomology, revealing torsion-free properties.

Findings

Stable rationality construction for Gushel-Mukai sixfolds

Integral cohomology is torsion-free for these varieties

Explicit cohomology computation results

Abstract

We provide a stable rationality construction for some smooth complex Gushel-Mukai varieties of dimension 6. As a consequence, we compute the integral singular cohomology of any smooth Gushel-Mukai sixfold and in particular, show that it is torsion-free.