Real Algebraic and Analytic Geometry
Submission: 2008, October 26.
Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-transitively on X, for all natural integers n. As an application we give a new and simpler proof of the fact that two rational nonsingular compact connected real algebraic surfaces are isomorphic if and only if they are homeomorphic as topological surfaces.
Mathematics Subject Classification (2000): 14P25, 14E07.
Keywords and Phrases: real algebraic surface; rational surface; geometrically rational surface; algebraic diffeomorphism; algebraic automorphism; transitive action.
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