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Introduction to Algebraic Curves
Phillip A. Griffiths, Institute for Advanced Study, Princeton, NJ

Translations of Mathematical Monographs
1989; 225 pp; softcover
Volume: 76
Reprint/Revision History:
fourth printing 2000
ISBN-10: 0-8218-4537-3
ISBN-13: 978-0-8218-4537-0
List Price: US$86
Member Price: US$68.80
Order Code: MMONO/76
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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.


"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

  • Fundamental concepts
  • The normalization theorem and its applications
  • The Riemann-Roch theorem
  • Applications of the Riemann-Roch theorem
  • Abel's theorem and its applications
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