We construct an explicit smooth Fano complex 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 PSL(2,F11)-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 PSL(2,F11)-action discovered by the second author in 2013.

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

Mongardi G.
2022

Abstract

We construct an explicit smooth Fano complex 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 PSL(2,F11)-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 PSL(2,F11)-action discovered by the second author in 2013.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/850328
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