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Gushel-Mukai varieties with many symmetries and an explicit irrational Gushel-Mukai threefold (2101.01959v1)
Published 6 Jan 2021 in math.AG
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.