Introduction to Algebraic Curves - Softcover

Phillip A. Griffiths

Softcover

ISBN 10: 0821845373 ISBN 13: 9780821845370

Publisher: American Mathematical Society, 1989

Synopsis

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.

About this title

Review

Gives an interesting overview of many of the deep problems in this field of mathematics ... a welcome monograph for both students and specialists working on harmonic analysis on Lie groups and homogeneous spaces." ---- Mathematical Reviews

Gives an interesting overview of the many problems in this field of mathematics--a welcome monograph for both students and specialists. -- G. Olafsson, Mathematical Reviews, 1997

Helgason sets a model of style and clarity that has not been matched since Enriques' "Geometria Projettiva". This is the kind of mathematics that will live forever. -- G-C. Rota, The Bulletin of Mathematical Books, Nov. 1994

The style is very fluent and pleasant, conducting the reader at a regular pace ... the present book will be a most valuable (and reasonably priced) reference for anyone interested in Radon transforms and analysis on semisimple Lie groups." -- --Bulletin of the AMS

Edition details

• Publisher: American Mathematical Society
• Publication date: 1989
• Language: English
• ISBN 10: 0821845373
• ISBN 13: 9780821845370
• Binding: Paperback
• Number of pages: 225