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Journal Articles Commentarii Mathematici Helvetici Year : 2020

Algebraic varieties are homeomorphic to varieties defined over number fields

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 $V$, produces a system of equations with algebraic coefficients of a variety homeomorphic to $V$

Dates and versions

hal-02536240 , version 1 (08-04-2020)

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Adam Parusinski, Guillaume Rond. Algebraic varieties are homeomorphic to varieties defined over number fields. Commentarii Mathematici Helvetici, 2020, 95, pp.339--359. ⟨10.4171/CMH/490⟩. ⟨hal-02536240⟩
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