Algebraic varieties are homeomorphic to varieties defined over number fields
Algebraic Geometry
2019-12-03 v2
Abstract
We show that every affine or projective algebraic variety defined over the field of real or complex numbers is homeomorphic to a variety defined over the field of algebraic numbers. We construct such a homeomorphism by choosing a small deformation of the coefficients of the original equations. This method is based on the properties of Zariski equisingular families of varieties. Moreover we construct an algorithm, that, given a system of equations defining a variety , produces a system of equations with algebraic coefficients of a variety homeomorphic to
Cite
@article{arxiv.1810.00808,
title = {Algebraic varieties are homeomorphic to varieties defined over number fields},
author = {Adam Parusinski and Guillaume Rond},
journal= {arXiv preprint arXiv:1810.00808},
year = {2019}
}
Comments
16 pages - to appear in Comment. Math. Helv