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In this article we study the transitivity of the group of automorphisms ofreal algebraic surfaces. We characterize real algebraic surfaces with verytransitive automorphism groups. We give applications to the classification ofreal algebraic models of compact surfaces: these applications yield new insightinto the geometry of the real locus, proving several surprising facts on thisgeometry. This geometry can be thought of as a half-way point between thebiregular and birational geometries.

Geometrically rational real conic bundles and very transitive actions