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