Download E-books Algebraic Curves and Riemann Surfaces (Graduate Studies in Mathematics, Vol 5) PDF

By Rick Miranda

During this booklet, 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 techniques should be introduced into play. consequently, many examples of algebraic curves are awarded within the first chapters. during this approach, the booklet starts as a primer on Riemann surfaces, with advanced charts and meromorphic services taking heart degree. however the major examples come from projective curves, and slowly yet definitely 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 application and naturalness are instantly visible. Requiring a history of a one semester of advanced variable! conception and a 12 months of summary algebra, this can be an outstanding graduate textbook for a second-semester direction in complicated variables or a year-long direction in algebraic geometry.

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