Complex algebraic curves

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Complex algebraic curves / Frances Kirwan

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 1992
形態:: viii, 264 p. ; 24 cm
シリーズ名:: London Mathematical Society student texts ; 23 <BA00194352>
著者名:: Kirwan, Frances Clare, 1959- <DA02752958>
ISBN:: 9780521412513 [052141251X] (: hard)
9780521423533 [0521423538] (: pbk)
書誌ID:: BA13776306

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注記:

Includes bibliographical references (p. 259-261) and index

主題:

Curves, Algebraic

言語:

英語

目次情報:

Introduction and background / 1：

A brief history of algebraic curves / 1.1：

Relationship with other parts of mathematics / 1.2：

Number theory / 1.2.1：

Singularities and the theory of knots / 1.2.2：

Complex analysis / 1.2.3：

Abelian integrals / 1.2.4：

Real Algebraic Curves / 1.3：

Hilbert's Nullstellensatz / 1.3.1：

Techniques for drawing real algebraic curves / 1.3.2：

Real algebraic curves inside complex algebraic curves / 1.3.3：

Important examples of real algebraic curves / 1.3.4：

Foundations / 2：

Complex algebraic curves in C[superscript 2] / 2.1：

Complex projective spaces / 2.2：

Complex projective curves in P[subscript 2] / 2.3：

Affine and projective curves / 2.4：

Exercises / 2.5：

Algebraic properties / 3：

Bezout's theorem / 3.1：

Points of inflection and cubic curves / 3.2：

Topological properties / 3.3：

The degree-genus formula / 4.1：

The first method of proof / 4.1.1：

The second method of proof / 4.1.2：

Branched covers of P[subscript 1] / 4.2：

Proof of the degree-genus formula / 4.3：

Riemann surfaces / 4.4：

The Weierstrass [weierp]-function / 5.1：

Differentials on Riemann surfaces / 5.2：

Holomorphic differentials / 6.1：

Abel's theorem / 6.2：

The Riemann-Roch theorem / 6.3：

Singular curves / 6.4：

Resolution of singularities / 7.1：

Newton polygons and Puiseux expansions / 7.2：

The topology of singular curves / 7.3：

Algebra / 7.4：

Topology / B：

Covering projections / C.1：

The genus is a topological invariant / C.2：

Spheres with handles / C.3：

Introduction and background / 1：

A brief history of algebraic curves / 1.1：

Relationship with other parts of mathematics / 1.2：

Number theory / 1.2.1：

Singularities and the theory of knots / 1.2.2：

Complex analysis / 1.2.3：

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