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平面代数曲线导引（影印版）

样章
作者：
Keith Kendig
定价：
99.00元
ISBN：
978-7-04-063238-5
版面字数：
345.00千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2025-02-07
物料号：
63238-00
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
  • 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
    • 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

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