Algebraic Curves and Riemann Surfaces - Rilegato

Miranda, Rick

Rilegato

ISBN 10: 0821802682 ISBN 13: 9780821802687

Casa editrice: Amer Mathematical Society, 1995

Riassunto

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 centre 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 Dualtiy 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 later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.

Su questo libro

Product Description:

Book by Rick Miranda

Su questa edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 1995
• ISBN 10: 0821802682
• ISBN 13: 9780821802687
• Rilegatura: Copertina rigida
• Numero di pagine: 390