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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.

Dates and versions

hal-01063471 , version 1 (12-09-2014)

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