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Rational real algebraic models of topological surfaces

Indranil Biswas·Johannes Huisman
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Abstract

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

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Indranil Biswas, Johannes Huisman. 2007-07-17. Rational real algebraic models of topological surfaces. https://arxiv.org/abs/math/0701402

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