论文标题
黎曼表面的轮廓
The Profiles of Riemann Surfaces
论文作者
论文摘要
考虑由代数，代数和逆函数设置的riemann表面。提出了一种描述这些Riemann表面的方法。每个这样的Riemann表面都分配给特殊类型的图形 - 配置文件。在图理论方面，阐明了概况存在的必要条件。配制了黎曼表面和轮廓之间一对一对应关系的条件。在图理论术语中，概况的存在标准是制定和证明的。结果标准可以用作具有设定签名的Riemann表面存在的标准。通过剖面描述Riemann表面的建议方法对应于Riemann表面作为Riemann球体上的覆盖面的直观概念。给出了代数函数的Riemann表面曲线和代数逆功能的Riemann表面曲线。
Riemann surfaces which are set by algebraic, algebroid and inverse functions are considered. A method for describing these Riemann surfaces by graphs is proposed. Each such Riemann surface is assigned to a special type of graph - profile. In terms of graph theory, the necessary and sufficient conditions of profile existence are clarified. The conditions of a one-to-one correspondence between Riemann surfaces and profiles are formulated. In the graph theory terminology the criterion of profiles existence is formulated and proved. The resulting criterion can be used as a criterion of existence of Riemann surfaces with a set signature. The proposed method of describing Riemann surfaces by profiles corresponds to the intuitive notion of a Riemann surface as a covering surface over a Riemann sphere. Examples of the Riemann surface profile of the algebraic function and the Riemann surface profile of the inverse function of algebroid are given.
