图书信息
图书目录
平面代数曲线导引（影印版）
暂无简介
作者：
Keith Kendig
定价：
99.00元
出版时间：
2025-02-07
ISBN：
978-7-04-063238-5
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
重点项目：
暂无
版面字数：
345.00千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 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
