Algebraic Curves and Riemann Surfaces (inbunden)

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Algebraisk geometri

Format: Inbunden (Hardback)
Språk: Engelska
Serie: Graduate Studies in Mathematics
Antal sidor: 390
Utgivningsdatum: 1995-04-30
Förlag: American Mathematical Society
Dimensioner: 260 x 185 x 30 mm
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ISBN: 9780821802687

Algebraic Curves and Riemann Surfaces

Name: Algebraic Curves and Riemann Surfaces
Price: 1615.00 SEK
Availability: InStock
Author: Rick Miranda
ISBN: 9780821802687

av Rick Miranda

Inbunden, Engelska, 1995-04-30

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In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. 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 a 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.

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Applications of Algebraic Geometry to Coding Theory, Physics and Computation

Ciro Ciliberto, Friedrich Hirzebruch, Rick Miranda, Mina Teicher

An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory...

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