# Rational real algebraic models of topological surfaces

### Indranil Biswas

School of Mathematics Département de Mathématiques Tata Institute of Fundamental Laboratoire CNRS UMR 6205 Research, Homi Bhabha Road Université de Bretagne Occidentale Mumbai 400005 6 avenue Victor Le Gorgeu CS 93837 India 29238 Brest cedex 3### Johannes Huisman

France

## Abstract

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.

## Cite this article

Indranil Biswas, Johannes Huisman, Rational real algebraic models of topological surfaces. Doc. Math. 12 (2007), pp. 549–567

DOI 10.4171/DM/234