Ebook: Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces

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.

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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.

Content:
Front Matter....Pages i-xiv
Categories, products, Projective and Inductive Limits....Pages 1-10
Basic Concepts of Homological Algebra....Pages 11-33
Sheaves....Pages 35-50
Cohomology of Sheaves....Pages 51-177
Compact Riemann surfaces and Abelian Varieties....Pages 179-280
Back Matter....Pages 281-290

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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.

Content:
Front Matter....Pages i-xiv
Categories, products, Projective and Inductive Limits....Pages 1-10
Basic Concepts of Homological Algebra....Pages 11-33
Sheaves....Pages 35-50
Cohomology of Sheaves....Pages 51-177
Compact Riemann surfaces and Abelian Varieties....Pages 179-280
Back Matter....Pages 281-290
....