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 carefully choosing a small deformation of the coefficients of the original equations. This deformation preserves all polynomial relations over $\mathbb Q$ satisfied by these coefficients and is equisingular in the sense of Zariski.

Moreover we construct an algorithm, that, given a system of equations defining a variety $V$, produces a system of equations with coefficients in $\bar{\mathbb Q}$ of a variety homeomorphic to $V$.

代数变种与定义在数字域上的变种同胚

亚当·帕鲁森斯基

纪尧姆·朗德

摘要

引用这篇文章