Real Algebraic and Analytic Geometry |

The group of automorphisms of a real rational surface is n-transitive.

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Submission: 2008, October 26.

*Abstract:
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.

**Full text**, 7p.:
pdf 120k.

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