双有理变换的起源、提出、理论建立和早期发展  

The Origin,Proposition,Theoretical Establishment and Early Development of Birational Transformation

作　　者：孙少朵 王淑红[1] SUN Shao-duo;WANG Shu-hong(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024

出　　处：《数学的实践与认识》2024年第9期222-232,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12271138,12171137)。

摘　　要：双有理变换是代数几何的重要内容之一,它的引入使得代数几何成为一门真正的学科,为之后许多研究领域提供了强大的工具.在文献分析和概念考证的基础上,对双有理变换的思想演变过程进行了研究.研究结果表明:阿波罗尼奥斯首先有了圆的反演变换的思想,黎曼明确提出双有理变换,迈出了曲线双有理变换研究的第一步.克雷莫纳系统阐述了平面图形的双有理几何变换,为双有理变换理论建立了主要框架,深刻影响了之后数学家对双有理变换的研究,促进了代数几何的发展.The birational transformation is one of the most important parts of algebraic geometry,and it had made algebraic geometry a true discipline,providing powerful tools for many subsequent research areas.On the basis of literature analysis and conceptual study the evolution of the idea of birational transformation is studied in this paper.The results show that Apollonius first had the idea of inverse transformations of circles,and Riemann explicitly proposed birational transformations,taking the first step in the study of birational transformations of curves.Cremona systematically described the birational geometric transformations of plane figures,established the main framework for the theory of birational transformations,profoundly influenced the subsequent mathematicians'research on birational transformations,and promoted the development of algebraic geometry.

关 键 词：双有理变换 路易吉·克雷莫纳 亏格 奇点 伯恩哈德·黎曼 马克斯·诺特 欧金尼奥·贝尔蒂尼 

分 类 号：O187[理学—数学]