《Complex Algebraic Curves》电子书下载

Complex Algebraic Curvestxt，chm，pdf，epub，mobi下载
作者: Frances Kirwan
出版社: Cambridge University Press
出版年: 1992-05-01
页数: 276
定价: USD 48.00
装帧: Paperback
丛书: London Mathematical Society Student Texts
ISBN: 9780521423533

内容简介 · · · · · ·

Complex algebraic curves were developed in the nineteenth century. They have many fascinating properties and crop up in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired by most undergraduate courses in mathematics, Dr Kirwan introduces the theory, observes the algebraic and...

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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