**Translations of Mathematical Monographs**

1989;
225 pp;
Softcover

MSC: Primary 14;
Secondary 30

Print ISBN: 978-0-8218-4537-0

Product Code: MMONO/76

List Price: $91.00

AMS Member Price: $72.80

MAA Member Price: $81.90

**Electronic ISBN: 978-1-4704-4490-7
Product Code: MMONO/76.E**

List Price: $91.00

AMS Member Price: $72.80

MAA Member Price: $81.90

# Introduction to Algebraic Curves

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*Phillip A. Griffiths*

Algebraic curves and compact Riemann surfaces comprise the most
developed and arguably the most beautiful portion of algebraic geometry.
However, the majority of books written on the subject discuss algebraic
curves and compact Riemann surfaces separately, as parts of distinct
general theories. Most texts and university courses on curve theory
generally conclude with the Riemann-Roch theorem, despite the fact that
this theorem is the gateway to some of the most fascinating results in
the theory of algebraic curves.

This book is based on a six-week series of lectures presented by the
author to third- and fourth-year undergraduates and graduate students at
Beijing University in 1982. The lectures began with minimal technical
requirements (a working knowledge of elementary complex function theory
and algebra together with some exposure to topology of compact surfaces)
and proceeded directly to the Riemann-Roch and Abel theorems. This book
differs from a number of recent books on this subject in that it
combines analytic and geometric methods at the outset, so that the
reader can grasp the basic results of the subject. Although such modern
techniques of sheaf theory, cohomology, and commutative algebra are not
covered here, the book provides a solid foundation to proceed to more
advanced texts in general algebraic geometry, complex manifolds, and
Riemann surfaces, as well as algebraic curves. Containing numerous
exercises and two exams, this book would make an excellent introductory
text.

#### Reviews & Endorsements

Altogether, the author achieves his intended goal of providing a solid but elementary foundation of the theory of algebraic curves and compact Riemann surfaces in a masterly way.

-- Mathematical Reviews

Very special introductory text on the theory of complex algebraic curves … Griffiths textbook will certainly maintain its timelessly unique character of being an excellent and thorough guide to the more advanced topics in algebraic curve theory.

-- Zentralblatt MATH

A nice introductory textbook on complex algebraic curves and compact Riemann surfaces … This volume is a good preparation for more advanced topics like sheaves and cohomology theory.

-- Monatshefte für Mathematik

#### Table of Contents

# Table of Contents

## Introduction to Algebraic Curves

- Cover Cover11
- Title page iii4
- English Translation of the Preface to the Chinese Edition v6
- Preface to the English Edition vii8
- Contents ix10
- Fundamental concepts 112
- The normalization theorem and its applications 5364
- The Riemann-Roch theorem 99110
- Applications of the Riemann-Roch theorem 125136
- Abel’s theorem and its applications 153164
- Test Problems I. (Chapters I and II) 207218
- Test Problems II. (Chapters III, IV and V) 209220
- Appendix. On a “General fact” 213224
- Annotated Bibliography 217228
- Index 221232
- Back Cover Back Cover1239