Gushel–Mukai varieties with many symmetries and an explicit irrational Gushel–Mukai threefold - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bollettino dell'Unione Matematica Italiana Année : 2021

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

Résumé

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, 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 PSL(2, F 11)-action discovered by the second author in 2013.
Fichier principal
Vignette du fichier
PSL11-v13-revised.pdf (519.29 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04463504 , version 1 (01-03-2024)

Identifiants

Citer

Olivier Debarre, Giovanni Mongardi. Gushel–Mukai varieties with many symmetries and an explicit irrational Gushel–Mukai threefold. Bollettino dell'Unione Matematica Italiana, 2021, 15 (1-2), pp.133 - 161. ⟨10.1007/s40574-021-00293-6⟩. ⟨hal-04463504⟩
9 Consultations
5 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More