By Rick Miranda
During this ebook, Miranda takes the process that algebraic curves are most sensible encountered for the 1st time over the complicated numbers, the place the reader's classical instinct approximately surfaces, integration, and different innovations will be introduced into play. for this reason, many examples of algebraic curves are provided within the first chapters. during this means, the e-book starts as a primer on Riemann surfaces, with complicated charts and meromorphic features taking heart 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 offered in an algebraic demeanour, through an model 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 history of a one semester of complicated variable! thought and a 12 months of summary algebra, this is often a superb graduate textbook for a second-semester direction in complicated variables or a year-long direction in algebraic geometry.
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