Algebraic Curves and Riemann Surfaces is popular PDF and ePub book, written by Rick Miranda in 1995, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Algebraic Curves and Riemann Surfaces can be Read Online from any device for your convenience.
Algebraic Curves and Riemann Surfaces Book PDF Summary
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 fromprojective 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 andcohomology 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.
Detail Book of Algebraic Curves and Riemann Surfaces PDF
- Author : Rick Miranda
- Release : 01 October 1995
- Publisher : American Mathematical Soc.
- ISBN : 9780821802687
- Genre : Mathematics
- Total Page : 414 pages
- Language : English
- PDF File Size : 8,8 Mb
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