By Rick Miranda

During this ebook, Miranda takes the technique 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 recommendations could be introduced into play. for this reason, many examples of algebraic curves are provided within the first chapters. during this means, the publication starts as a primer on Riemann surfaces, with advanced charts and meromorphic services taking middle degree. however the major examples come from projective curves, and slowly yet without doubt the textual content strikes towards the algebraic type. Proofs of the Riemann-Roch and Serre Duality Theorems are provided in an algebraic demeanour, through an version of the adelic facts, expressed thoroughly by way of fixing a Mittag-Leffler challenge. Sheaves and cohomology are brought as a unifying gadget within the latter chapters, in order that their software and naturalness are instantly visible. Requiring a history of a one semester of advanced variable! thought and a yr of summary algebra, this can be a superb graduate textbook for a second-semester path in advanced variables or a year-long path in algebraic geometry.

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