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arXiv · 2101.01959

Gushel-Mukai varieties with many symmetries and an explicit irrational Gushel-Mukai threefold

Olivier Debarre·Giovanni Mongardi
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Abstract

We construct an explicit complex smooth Fano threefold with Picard number 1, index 1, and degree 10 (also known as a Gushel-Mukai threefold) and prove that it is not rational by showing that its intermediate Jacobian has a faithful $\mathrm{PSL}(2,\mathbf{F}_{11}) $-action. Along the way, we construct Gushel-Mukai varieties of various dimensions with rather large (finite) automorphism groups. The starting point of all these constructions is an Eisenbud-Popescu-Walter sextic with a faithful $\mathrm{PSL}(2,\mathbf{F}_{11}) $-action discovered by the second author in 2013.

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Olivier Debarre, Giovanni Mongardi. 2021-01-06. Gushel-Mukai varieties with many symmetries and an explicit irrational Gushel-Mukai threefold. https://arxiv.org/abs/2101.01959

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