About this product

Product Identifiers

PublisherAmerican Mathematical Society

ISBN-100821802682

ISBN-139780821802687

eBay Product ID (ePID)407329

Product Key Features

Number of Pages390 Pages

LanguageEnglish

Publication NameAlgebraic Curves and Riemann Surfaces

Publication Year1995

SubjectGeometry / Algebraic, Mathematical Analysis

TypeTextbook

AuthorRick Miranda

Subject AreaMathematics

SeriesGraduate Studies in Mathematics Ser.

FormatHardcover

Dimensions

Item Height1.1 in

Item Weight30.7 Oz

Item Length10.3 in

Item Width7.3 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN95-001947

Dewey Edition20

Series Volume Number5

Dewey Decimal516.3/52

Table Of ContentRiemann surfaces: Basic definitions; Functions and maps; More examples of Riemann surfaces; Integration on Riemann surfaces; Divisors and meromorphic functions; Algebraic curves and the Riemann-Roch theorem; Applications of Riemann-Roch; Abel's theorem; Sheaves and Cech cohomology; Algebraic sheaves; Invertible sheaves, line bundles, and $\check H^1$; References; Index of notation; Index of terminology.

SynopsisTakes 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. This book covers Riemann surfaces, with complex charts and meromorphic functions taking center stage., 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 centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy 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 andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry., 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.

LC Classification NumberQA565.M687 1995