Algebraic varieties are homeomorphic to varieties defined over number fields - Archive ouverte HAL Access content directly
Journal Articles Commentarii Mathematici Helvetici Year : 2020

## Algebraic varieties are homeomorphic to varieties defined over number fields

• Function : Author
Guillaume Rond

#### 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 $V$

#### Domains

Mathematics [math] Algebraic Geometry [math.AG]

### Dates and versions

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

### Identifiers

• HAL Id : hal-02536240 , version 1
• ARXIV :
• DOI :

### Cite

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⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

58 View