English

Rational real algebraic models of topological surfaces

Algebraic Geometry 2007-07-17 v2

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.

Keywords

Cite

@article{arxiv.math/0701402,
  title  = {Rational real algebraic models of topological surfaces},
  author = {Indranil Biswas and Johannes Huisman},
  journal= {arXiv preprint arXiv:math/0701402},
  year   = {2007}
}

Comments

21 pages; LaTeX; complete revision of version 1

R2 v1 2026-07-22T17:49:20.751Z