# Real structures on rational surfaces and automorphisms acting trivially on Picard groups

Abstract : In this article, we prove that any complex smooth rational surface X which cannot be obtained by blowing up $\mathbb P^2_{\mathbb C}$ at $r\geq 10$ points has a finite number of real forms, owing to simple results about the group $\mathrm{Aut}^{\#}X$ of complex automorphisms of X which act trivially on the Picard group of X.
Type de document :
Pré-publication, Document de travail
8 pages. 2014

https://hal.archives-ouvertes.fr/hal-01063471
Contributeur : Mohamed Benzerga <>
Soumis le : vendredi 12 septembre 2014 - 11:10:53
Dernière modification le : mercredi 19 décembre 2018 - 14:08:04

### Identifiants

• HAL Id : hal-01063471, version 1
• ARXIV : 1409.3490

### Citation

Mohamed Benzerga. Real structures on rational surfaces and automorphisms acting trivially on Picard groups. 8 pages. 2014. 〈hal-01063471〉

### Métriques

Consultations de la notice