平面代数曲线导引（影印版）

样章

作者：

Keith Kendig

定价：

99.00 元

版面字数：

345千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2025年

ISBN：

978-7-04-063238-5

物料号：

63238-00

出版时间：

2025-02-07

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

代数几何学

暂无

目录
- 前辅文
- 1 A Gallery of Algebraic Curves
  - 1.1 Curves of Degree One and Two
  - 1.2 Curves of Degree Three and Higher
  - 1.3 Six Basic Cubics
  - 1.4 Some Curves in Polar Coordinates
  - 1.5 Parametric Curves
  - 1.6 The Resultant
  - 1.7 Back to an Example
  - 1.8 Lissajous Figures
  - 1.9 Morphing Between Curves
  - 1.10 Designer Curves
- 2 Points at Infinity
  - 2.1 Adjoining Points at Infinity
  - 2.2 Examples
  - 2.3 A Basic Picture
  - 2.4 Basic Definitions
  - 2.5 Further Examples
- 3 From Real to Complex
  - 3.1 Definitions
  - 3.2 The Idea of Multiplicity; Examples
  - 3.3 A Reality Check
  - 3.4 A Factorization Theorem for Polynomials in C[x,y]
  - 3.5 Local Parametrizations of a Plane Algebraic Curve
  - 3.6 Definition of Intersection Multiplicity for Two Branches
  - 3.7 An Example
  - 3.8 Multiplicity at an Intersection Point of Two Plane Algebraic Curves
  - 3.9 Intersection Multiplicity Without Parametrizations
  - 3.10 Bézout's theorem
  - 3.11 Bézout's theorem Generalizes the Fundamental Theorem of Algebra
  - 3.12 An Application of Bézout's theorem: Pascal's theorem
- 4 Topology of Algebraic Curves in P2(C)
  - 4.1 Introduction
  - 4.2 Connectedness
  - 4.3 Algebraic Curves are Connected
  - 4.4 Orientable Two-Manifolds
  - 4.5 Nonsingular Curves are Two-Manifolds
  - 4.6 Algebraic Curves are Orientable
  - 4.7 The Genus Formula
- 5 Singularities
  - 5.1 Introduction
  - 5.2 Definitions and Examples
  - 5.3 Singularities at Infinity
  - 5.4 Nonsingular Projective Curves
  - 5.5 Singularities and Polynomial Degree
  - 5.6 Singularities and Genus
  - 5.7 A More General Genus Formula
  - 5.8 Non-Ordinary Singularities
  - 5.9 Further Examples
  - 5.10 Singularities versus Doing Math on Curves
  - 5.11 The Function Field of an Irreducible Curve
  - 5.12 Birational Equivalence
  - 5.13 Examples of Birational Equivalence
  - 5.14 Space-Curve Models
  - 5.15 Resolving a Higher-Order Ordinary Singularity
  - 5.16 Examples of Resolving an Ordinary Singularity
  - 5.17 Resolving Several Ordinary Singularities
  - 5.18 Quadratic Transformations
- 6 The Big Three: C, K, S
  - 6.1 Function Fields
  - 6.2 Compact Riemann Surfaces
  - 6.3 Projective Plane Curves
  - 6.4 f, f2, f: Curves and Function Fields
  - 6.5 g1, g2, g: Compact Riemann Surfaces and Curves
  - 6.6 h1, h2, h: Function Fields and Compact Riemann Surfaces
  - 6.7 Genus
  - 6.8 Genus 0
  - 6.9 Genus One
  - 6.10 An Analogy
  - 6.11 Equipotentials and Streamlines
  - 6.12 Differentials Generate Vector Fields
  - 6.13 A Major Difference
  - 6.14 Divisors
  - 6.15 The Riemann-Roch theorem
- Bibliography
- Index
- About the Author