Translations of Mathematical Monographs 1989; 225 pp; softcover Volume: 76 Reprint/Revision History: fourth printing 2000 ISBN10: 0821845373 ISBN13: 9780821845370 List Price: US$86 Member Price: US$68.80 Order Code: MMONO/76
 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 RiemannRoch 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 sixweek series of lectures presented by the author to third and fourthyear 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 RiemannRoch 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 "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 RiemannRoch theorem
 Applications of the RiemannRoch theorem
 Abel's theorem and its applications
