基本説明
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.
Description
(Text)
Dieses Buch ist aus einer Reihe von Vorlesungen an der Universität Bonn entstanden, die sich an Studierende im Hauptstudium wandte. Es beginnt mit einer Einführung in die homologische Algebra, die Garbentheorie und die Kohomologie von Garben. Darauf aufbauend kommt eine Einführung in die moderne algebraische Geometrie.
(Table of content)
Aus dem Inhalt:
Categories, Products, Projective and Inductive Limits
- Basic Concepts of Homological Algebra
- Presheaves and Sheaves
- Cohomology of Sheaves
- Compact Riemann surfaces and Abelian Varieties
(Text)
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.
