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.
Debarre O., Mongardi G. (2022). Gushel–Mukai varieties with many symmetries and an explicit irrational Gushel–Mukai threefold. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 15(1-2), 133-161 [10.1007/s40574-021-00293-6].
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.| File | Dimensione | Formato | |
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