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Springer Spektrum - Mathematik - Geometrie & Topologie | Lectures on Algebraic Geometry I - Sheaves, Cohomology of Sheaves, and Applications to Riemann

Lectures on Algebraic Geometry I

Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces

Series: Aspects of Mathematics, Vol. 35

Harder, Günter

2nd überarb. ed. 2012, XIII, 301 p.

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  • Algebraische Geometrie: Von Abel und Riemann bis heute
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own.
In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.

Content Level » Research

Keywords » Algebraische Geometrie - Garbe (Math.) - Homologische Algebra - Kohomologie - Kommutative Algebra - Komplexe Analysis

Related subjects » Algebra - Geometrie & Topologie

Table of contents 

Categories, Products, Projective and Inductive Limits - Basic Concepts of Homological Algebra - Sheaves - Cohomology of Sheaves - Compact Riemann surfaces and Abelian Varieties

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