Tojagor Fran Burstall added it Jan 04, The text grew out of lecture notes for courses which the author has taught several times during the last ten years. Home Questions Tags Users Unanswered. In what ways can an algebraic curve be embedded in a larger ambient space, such as the plane? Can they be classified? Meromorphic functions on smooth projective curves M Feb 8 9. The hyperelliptic case is not hard to understand.
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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 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. Readership Graduate students studying complex variables and algebraic geometry.
Now, in its evolved and fully ripe form, the text impressively reflects his apparently outstanding teaching skills as well as his admirable ability for combining great expertise in the field with masterly aptitude for representation and didactical sensibility.
This book is by far much more than just another text on algebraic curves, among several others, for it offers many new and unique features … one prominent feature is provided by the fact that the analytic viewpoint Riemann surfaces and the algebraic aspect projective curves are discussed in a well-balanced fashion … A wealth of concrete examples … enhance the rich theoretical material developed in the course of the exposition, very much so to the benefit of the reader.
Another advantage of this excellent text is provided by the pleasant and vivid manner of writing … Altogether, the present book is a masterly written, irresistible invitation to complex algebraic geometry and its generalization to the rich theory of algebraic schemes … The present book is perfectly suited for graduate students, partly even for senior undergraduate students, for self-teaching non-experts, and also—as an extraordinarily inspiring source and reference book—for teachers and researchers.
The price of the book is very affordable. The exercises were well chosen, and served to give further examples and developments of the theory.
ALGEBRAIC CURVES AND RIEMANN SURFACES MIRANDA PDF
Algebraic Curves and Riemann Surfaces