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 $V$

中文翻译：

---

代数簇同胚定义在数域上的簇

我们表明，在实数或复数域上定义的每一个仿射或射影代数簇都同胚于在代数数域上定义的簇。我们通过选择原始方程系数的小变形来构造这样的同胚。该方法基于 Zariski equisingular 品种家族的特性。此外，我们构建了一个算法，该算法给定一个定义变量 $V$ 的方程组，生成一个方程组，该方程组的代数系数同胚为 $V$