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

Mohamed Benzerga (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Domaines: Géométrie algébrique [math.AG]

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