Rational Real Algebraic Models of Topological Surfaces

Comessatti proved that the set of all real points of a rational real algebraic surface is either a nonorientable surface, or diffeomorphic to the sphere or the torus. Conversely, it is well known that each of these surfaces admits at least one rational real algebraic model. We prove that they admit exactly one rational real algebraic model. This was known earlier only for the sphere, the torus, the real projective plane and the Klein bottle.

2000 Mathematics Subject Classification: 14P25, 14E07

Keywords and Phrases: Real algebraic surface, topological surface, rational surface, rational model, birational map, algebraic diffeomorphism, transitivity, geometrically rational surface, geometrically rational model

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