Linear equations on real algebraic surfaces
Algebraic Geometry
2016-04-27 v2
Abstract
We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a continuous rational solution. This is known to fail in higher dimensions.
Cite
@article{arxiv.1602.01986,
title = {Linear equations on real algebraic surfaces},
author = {Wojciech Kucharz and Krzysztof Kurdyka},
journal= {arXiv preprint arXiv:1602.01986},
year = {2016}
}