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Riemann Surfaces Graduate Texts In Mathematics Series , Second Edition Books Textbooks Low-priced

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Riemann Surfaces(Graduate Texts in Mathematics Series), Second Edition Books Textbooks low-priced



Author John B.Conway

Publisher World Publishing Corporation

Isbn 7506259478

Published Sep 2003

Pages 363

Size 24k

Edition 2nd

Format Paperback

Language English

Page material gelatine plate paper

Shop price: $18.20

Product Description:

It is gratifying to learn that there is new life in an old field that has been at the center of one's existence for over a quarter of a century. It is particularly pleasing that the subject of Riemann surfaces has attracted the attention of a new generation of mathematicians from (newly) adjacent fields (for example, those interested in hyperbolic manifolds and iterations of rational maps) and young physicists who have been convinced (certainly not by mathematicians) that compact Riemann surfaces may play an important role in their (string) universe. We hope that non-mathematicians as well as mathematicians (working in nearby areas to the central topic of this book) will also learn part of this subject for the sheer beauty and elegance of the material (work of Weierstrass, Jacobi, Riemann, Hilbert, Weyl) and as healthy exposure to the way (some) mathematicians write about mathematics.


Preface to the Second Edition

Preface to the First Edition

Commonly Used Symbols

Chapter 0

An Overview

0.1. Topological Aspects, Uniformization, and Fuchsian Groups

0.2. Algebraic Functions

0.3. Abelian Varieties

0.4. More Analytic Aspects

Chapter i

Riemann Surfaces

I.1. Definitions and Examples

I.2. Topology of Riemann Surfaces

I.3. Differential Forms

I.4. Integration Formulae

Chapter ii

Existence Theorems

II.1. Hilbert Space Theory--A Quick Review

II.2. Weyl's Lemma

II.3. The Hilbert Space of Square lntegrable Forms

.II.4. Harmonic Differentials

II.5. Meromorphic Functions and Differentials

Chapter iii

Compact Riemann Surfaces

IlI.1. Intersection Theory on Compact Surfaces

III.2. Harmonic and Analytic Differentials on Compact Surfaces

III.3. Bilinear Relations

III.4. Divisors and the Riemann-Roch Theorem

III.5. Applications of the Riemann-Roch Theorem

III.6. Abel's Theorem and the Jacobi Inversion Problem

III.7. Hyperelliptic Riemann Surfaces

III.8. Special Divisors on Compact Surfaces

III.9. Multivalued Functions

III.10. Projective Imbeddings

III.11. More on the Jacobian Variety

III.12. Torelli's Theorem

Chapter iv


IV.1. More on Harmonic Functions (A Quick Review)

IV.2. Subharmonic Functions and Perron's Method

IV.3. A Classification of Riemann Surfaces

IV.4. The Uniformization Theorem for Simply Connected Surfaces

IV.5. Uniformization of Arbitrary Riemann Surfaces

IV.6. The Exceptional Riemann Surfaces

IV.7. Two Problems on Moduli

IV.8. Riemannian Metrics

IV.9. Discontinuous Groups and Branched Coverings

IV.10. Riemann-Roch--An Alternate Approach

IV.11. Algebraic Function Fields in One Variable

Chapter v

Automorphisms of Compact Surfaces--Elementary Theory

V.1. Hurwitz's Theorem

V.2. Representations of the Automorphism Group on

Spaces of Differentials

V.3. Representation of Aut M on Hi(M)

V.4. The Exceptional Riemann Surfaces

Chapter vi

Theta Functions

VI.1. The Riemann Them Function

VI.2. The Theta Functions Associated with a Riemann Surface

VI.3. The Theta Divisor

Chapter vii


VII.1. Hyperelliptic Surfaces (Once Again)

VII.2. Relations Among Quadratic Differentials

VII.3. Examples of Non-hyperelliptic Surfaces

VII.4. Branch Points of Hyperelliptic Surfaces as Holomorphic

Functions of the Periods

VII.5. Examples of Prym Differentials

VII.6. The Trisecant Formula



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