# 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.

https://hal.archives-ouvertes.fr/hal-01063471
Contributor : Mohamed Benzerga <>
Submitted on : Friday, September 12, 2014 - 11:10:53 AM
Last modification on : Monday, March 9, 2020 - 6:15:54 PM

### Identifiers

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

### Citation

Mohamed Benzerga. Real structures on rational surfaces and automorphisms acting trivially on Picard groups. 2014. ⟨hal-01063471⟩

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