On the cohomology of Gushel-Mukai sixfolds
Olivier Debarre, Alexander Kuznetsov

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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Advanced Combinatorial Mathematics
