Algebraic Curves and Riemann Surfaces
American Mathematical Soc., 1995 - 390 pages
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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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, ...
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R. Miranda: Algebraic curves and Riemann surfaces, Graduate Studies in Mathematics 5, American Mathematical Society 1995. O.Forster: Lectures on Riemann ...
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Math 4300/6300 (Algebraic Curves) Fall 2003
Algebraic Curves and Riemann Surfaces. AMS, Graduate Studies in Mathematics, Vol. 5 (1995). T.~Shifrin. Abstract Algebra: A Geometric Approach. ...
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The main textbook for this course is Algebraic Curves and Riemann Surfaces by Rick Miranda, Graduate Studies in Mathematics, Volume 5, AMS (1995). ...
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Algebraic curves and Riemann surfaces (graduate studies in mathematics, 5). Auteur(s) : MIRANDA Rick Date de parution: 01-1995 Langue : ANGLAIS ...
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In my whole 20+ year career of teaching graduate courses in algebraic curves and Riemann surfaces at a big state school, I cannot ever remember having a ...
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