By Rick Miranda

ISBN-10: 0821802682

ISBN-13: 9780821802687

During this e-book, Miranda takes the method that algebraic curves are most sensible encountered for the 1st time over the advanced numbers, the place the reader's classical instinct approximately surfaces, integration, and different ideas may be introduced into play. for this reason, many examples of algebraic curves are awarded within the first chapters. during this method, the booklet starts as a primer on Riemann surfaces, with advanced charts and meromorphic features taking middle level. however the major examples come from projective curves, and slowly yet definitely the textual content strikes towards the algebraic class. Proofs of the Riemann-Roch and Serre Duality Theorems are provided in an algebraic demeanour, through an variation of the adelic evidence, expressed thoroughly when it comes to fixing a Mittag-Leffler challenge. Sheaves and cohomology are brought as a unifying equipment within the latter chapters, in order that their application and naturalness are instantly noticeable. Requiring a historical past of a one semester of advanced variable! idea and a 12 months of summary algebra, this can be a superb graduate textbook for a second-semester direction in advanced variables or a year-long path in algebraic geometry.

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### Algebraic Curves and Riemann Surfaces by Rick Miranda

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