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.
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