Algebraic Curves and Riemann Surfaces by Rick Miranda

Algebraic Curves and Riemann Surfaces by Rick Miranda

In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage.But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Duality Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves and cohomology are introduced as a unifying device in the latter chapters, so that their utility and naturalness are immediately obvious. Requiring a background of a one semester of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-semester course in complex variables or a year-long course in algebraic geometry.

SKU	Unavailable
ISBN 13	9780821802687
ISBN 10	0821802682
Title	Algebraic Curves and Riemann Surfaces
Author	Rick Miranda
Series	Graduate Studies In Mathematics
Condition	Unavailable
Binding Type	Hardback
Publisher	American Mathematical Society
Year published	1995-04-30
Number of pages	390
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.