Description

Book Synopsis
Algebraic curves have many special properties that make their study rewarding. This work presents the various aspects of curves and emphasizes connections with algebra. It covers topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups.

Table of Contents
Algebraic Preliminaries From algebra to geometry Geometry of dimension one Divisors and line bundles Vector bundles, coherent sheaves, and cohomology Vector bundles on $\mathbb{P}^{1}$ General theory of curves Elliptic curves The Riemann-Roch theorem Curves over arithmetic fields Bibliography Index.

Algebraic Curves and Onedimensional Fields

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    A Paperback by American Mathem American Mathem

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      Book details

      Publisher American Mathematical Society
      Published 10/30/2002 12:00:00 AM
      ISBN-13 9780821828625
      978-0821828625
      ISBN-10 0821828622

      Description

      Book Synopsis
      Algebraic curves have many special properties that make their study rewarding. This work presents the various aspects of curves and emphasizes connections with algebra. It covers topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups.

      Table of Contents
      Algebraic Preliminaries From algebra to geometry Geometry of dimension one Divisors and line bundles Vector bundles, coherent sheaves, and cohomology Vector bundles on $\mathbb{P}^{1}$ General theory of curves Elliptic curves The Riemann-Roch theorem Curves over arithmetic fields Bibliography Index.

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