Structures réelles sur les surfaces rationnelles

Abstract : The aim of this PhD thesis is to give a partial answer to the finiteness problem for R-isomorphism classes of real forms of any smooth projective complex rational surface X, i.e. for the isomorphism classes of R-schemes whose complexification is isomorphic to X. We study this problem in terms of real structures (or antiholomorphic involutions, which generalize complex conjugation) on X: the advantage of this approach is that it helps us rephrasing our problem with automorphism groups of rational surfaces, via Galois cohomology. Thanks to recent results on these automorphism groups, using hyperbolic geometry and, to a lesser extent, holomorphic dynamics and metric geometry, we prove several finiteness results which go further than Del Pezzo surfaces and can apply to some rational surfaces with large automorphism groups.
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Mohamed Benzerga. Structures réelles sur les surfaces rationnelles. Géométrie algébrique [math.AG]. Université d'Angers, 2016. Français. ⟨tel-01471071⟩

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