Description

Book Synopsis
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. This book covers Riemann surfaces, with complex charts and meromorphic functions taking center stage.

Table of Contents
Riemann 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.

Algebraic Curves and Riemann Surfaces

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    A Hardback by Rick Miranda

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      Publisher: American Mathematical Society
      Publication Date: Publication Date: 30/04/1995
      ISBN13: 9780821802687, 978-0821802687
      ISBN10: 0821802682

      Description

      Book Synopsis
      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. This book covers Riemann surfaces, with complex charts and meromorphic functions taking center stage.

      Table of Contents
      Riemann 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.

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