论文标题
真实代数品种的seminalization的概念
A notion of seminormalization for real algebraic varieties
论文作者
论文摘要
代数品种$ x $的半正态化是与有限的，男子式和公约的形态与$ x $相关的最大品种。在本文中，我们介绍了适用于真实代数品种的符号化的变体，称为r-脱粒化。该对象具有相同类型的符号化的通用属性，但与多样性的真实闭合点有关。在上一篇论文中，作者使用有理函数研究了复杂代数品种的符号化，这些函数不断扩展到欧几里得拓扑的封闭点。我们在这里适应其中一些结果，以适应R-骨化规范化，并提供了几个示例。我们还表明，R-Seminalatorization通过标准化纯粹的复杂点并将真实点归一化来改变实际品种的奇异性。
The seminormalization of an algebraic variety $X$ is the biggest variety linked to $X$ by a finite, birational and bijective morphism. In this paper we introduce a variant of the seminormalization, suited for real algebraic varieties, called the R-seminormalization. This object have a universal property of the same kind of the one of the seminormalization but related to the real closed points of the variety. In a previous paper, the author studied the seminormalization of complex algebraic varieties using rational functions that extend continuously to the closed points for the Euclidean topology. We adapt here some of those results to the R-seminormalization and we provide several examples. We also show that the R-seminormalization modifies the singularities of a real variety by normalizing the purely complex points and seminormalizing the real ones.
