The biLipschitz Geometry of Complex Curves: An Algebraic Approach

被引：1

作者：

Giles Flores, Arturo ^{[1
]}

Nogueira da Silva, Otoniel ^{[2
]}

Teissier, Bernard ^{[3
]}

机构：

[1] Univ Autonoma Aguascalientes, Dept Matemat & Fis, Aguascalientes, Aguascalientes, Mexico

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Cuernavaca, Morelos, Mexico

[3] Inst Math Jussieu Paris Rive Gauche, Paris, France

来源：

INTRODUCTION TO LIPSCHITZ GEOMETRY OF SINGULARITIES | 2020年 / 2280卷

关键词：

LOCAL-RINGS; EQUISINGULARITY; SINGULARITIES; DEFORMATIONS; SATURATION; NUMBER;

D O I：

10.1007/978-3-030-61807-0_8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of these notes is to explain why a generic projection to a plane of a reduced germ of complex analytic space curve is a bi-Lipschitz homeomorphismfor the outer metric. This is related to the fact that all topologically equivalent germs of plane curves are exactly the generic projections of a single germ of a space curve. The analytic algebra of this germ is the algebra of Lipschitz meromorphic functions on any of its generic projections. An application to the Lipschitz geometry of polar curves is given.

引用

页码：217 / 271

页数：55

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