《复代数曲线》电子书下载

复代数曲线txt,chm,pdf,epub,mobi下载
作者:Frances Kirwan（柯万）
出版社: 世界图书出版公司
副标题: Complex Algebraic Curves(London Mathematical Society Students Texts 23)
原作名: complex algebraic curves
出版年: 2008-5
页数: 264 页
定价: 29.00元
装帧: 平装
ISBN: 9787506292030

内容简介 · · · · · ·

中译名：复代数曲面

世图书号： 978-7-5062-9203-0

原版书号： 978-0-521-42353-3

原出版社： Cambridge University Press

原版出版年代： 1992年

世图影印年代： 2008年

目录及部分内容页要览：

19世纪发展起来的复代数曲面理论,其良好的性质已经在数学的各个领域以及理论物理学中得到很好的应用,成为许多科目研究中心话题。本书源自Kirwan 在牛津大学的讲义,作者以本科生掌握的数学知识为基础引入了该理论,详细介绍了复代数曲面的代数和拓扑性质以及它们和复分析的联系。本书适于数学专业本科高年级研究生以及相关专业的研究人员。

目次：背景；基础知识；代数性质；拓扑性质；黎曼面；黎曼面上的微分；奇异曲面。

作者简介 · · · · · ·

Dame Frances Clare Kirwan, DBE FRS (born 1959) is a British mathematician, currently a Professor of Mathematics at the University of Oxford. Her fields of specialisation are algebraic and symplectic geometry.

http://en.wikipedia.org/wiki/Frances_Kirwan

https://www.maths.ox.ac.uk/people/profiles/frances.kirwan

目录 · · · · · ·

1 Introduction and background
1.1 A brief history of algebraic curves
1.2 Relationship with other parts of mathematics
1.2.1 Number theory
1.2.2 Singularities and the theory of knots
1.2.3 Complex analysis
· · · · · ·()
1 Introduction and background
1.1 A brief history of algebraic curves
1.2 Relationship with other parts of mathematics
1.2.1 Number theory
1.2.2 Singularities and the theory of knots
1.2.3 Complex analysis
1.2.4 Abelian integrals
1.3 Real Algebraic Curves
1.3.1 Hilbert's Nullstellensatz
1.3.2 Techniques for drawing real algebraic curves
1.3.3 Real algebraic curves inside complex algebraic curves
1.3.4 Important examples of real algebraic curves
2 Foundations
2.1 Complex algebraic curves in Cs
2.2 Complex projective spaces
2.3 Complex projective curves in Ps
2.4 Affine and projective curves
2.5 Exercises
3 Algebraic properties
3.1 Bezout's theorem
3.2 Points of inflection and cubic curves
3.3 Exercises
4 Topological properties
4.1 The degree-genus formula
4.1.1 The first method of proof
4.1.2 The second method of proof
4.2 Branched covers of PI
4.3 Proof of the degree-genus formula
4.4 Exercises
5 Riemann surfaces
5.1 The Weierstrass function
5.2 Riemann surfaces
5.3 Exercises
6 Differentials on Riemann surfaces
6.1 Holomorphic differentials
6.2 Abel's theorem
6.3 The Riemann-Roch theorem
6.4 Exercises
7 Singular curves
7.1 Resolution of Singularities
7.2 Newton polygons and Puiseux expansions
7.3 The topology of singular curves
7.4 Exercises
A Algebra
B Complex analysis
C Topology
C.1 Covering projections
C.2 The genus is a topological invariant
C.3 Spheres with handles
· · · · · · ()

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