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arXiv · 1409.3490

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

Mohamed Benzerga
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Abstract

In this article, we prove that any complex smooth rational surface $X$ which has no automorphism of positive entropy has a finite number of real forms (this is especially the case if $X$ cannot be obtained by blowing up $\mathbb P^2_{\mathbb C}$ at $r\geq 10$ points). In particular, we prove that the group $\mathrm{Aut}^{\#}X$ of complex automorphisms of $X$ which act trivially on the Picard group of $X$ is a linear algebraic group defined over $\mathbb R$.

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Mohamed Benzerga. 2015-11-13. Real structures on rational surfaces and automorphisms acting trivially on Picard groups. https://doi.org/10.1007/s00209-015-1581-x

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