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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.
For this second edition the text was completely revised and corrected. The author also added a short section on moduli of elliptic curves with N-level structures. This new paragraph anticipates some of the techniques of volume II.
List of contents
Categories, Products, Projective and Inductive Limits - Basic Concepts of Homological Algebra - Sheaves - Cohomology of Sheaves - Compact Riemann surfaces and Abelian Varieties
About the author
Prof. Dr. Günter Harder, Max-Planck-Institute for Mathematics, Bonn
Summary
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.
For this second edition the text was completely revised and corrected. The author also added a short section on moduli of elliptic curves with N-level structures. This new paragraph anticipates some of the techniques of volume II.
Foreword
Abel, Jacobi and Riemann from todays point of view.
Additional text
"No doubt, the great lucidity of exposition, the masterly style of writing, the broad spectrum of topics touched upon, and the purposeful, very special disposition of the subject matter make this text, together with its expected companion book(s), a very particular and outstanding enrichment of the existing textbook literature in algebraic geometry and its intimately related areas."
Zentralblatt MATH Zbl 1129.14001
Report
"No doubt, the great lucidity of exposition, the masterly style of writing, the broad spectrum of topics touched upon, and the purposeful, very special disposition of the subject matter make this text, together with its expected companion book(s), a very particular and outstanding enrichment of the existing textbook literature in algebraic geometry and its intimately related areas." Zentralblatt MATH Zbl 1129.14001
