论文标题
代数品种之间同构的代数表征
Algebraic characterizations of homeomorphisms between algebraic varieties
论文作者
论文摘要
我们解决了一个问题的问题，即在代数封闭的特征零字段上，代数品种之间的形态分别是等效的，这是Zariski拓扑的同态和我们引入强大的拓扑的同态。我们的答案涉及对代数品种之间形态的拟态化和饱和度的研究，以及在代数品种的闭合点上的持续合理功能的解释。连续性是指在复杂情况下通常是通常的欧几里得拓扑结构的强大拓扑结构，而它来自真实封闭领域的理论。
We address the question of finding algebraic properties that are respectively equivalent, for a morphism between algebraic varieties over an algebraically closed field of characteristic zero, to be an homeomorphism for the Zariski topology and for a strong topology that we introduce. Our answers involve a study of seminormalization and saturation for morphisms between algebraic varieties, together with an interpretation in terms of continuous rational functions on the closed points of an algebraic variety. The continuity refers to the strong topology which is the usual Euclidean topology in the complex case, whereas it comes from the theory of real closed fields otherwise.
