Algebraic Curves and Riemann Surfaces

American Mathematical Soc., 1995 - 390 pages
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The author of this monograph argues 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 a graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.

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Page 374 - W. Massey, A basic course in algebraic topology. Graduate Texts in Mathematics 127, Springer- Verlag, New York 1991.

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Algebraic curves and Riemann surfaces , by Rick Miranda, Graduate ...
Algebraic curves and Riemann surfaces, by Rick Miranda, Graduate Studies in. Math., vol. 5, Amer. Math. Soc., Providence, RI, 1995, xxi+390 pp., $59.00, ... bull/ 1996-33-02/ S0273-0979-96-00636-2/ S0273-0979-96-00636-2.pdf : Download files / Some more ...
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Algebraic Curves and Riemann Surfaces. AMS, Graduate Studies in Mathematics, Vol. 5 (1995). T.~Shifrin. Abstract Algebra: A Geometric Approach. ... ~rulla/ M6300.html

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