Lectures on algebraic geometry I : sheaves, cohomology of sheaves, and applications to riemann surfaces
Harder, Gunter
Lectures on algebraic geometry I : sheaves, cohomology of sheaves, and applications to riemann surfaces - 2nd rev ed. - Wiesbaden : Vieweg+Teubner Verlag, 2011. - xiii, 299p. - Aspects of mathematics. E ; v. 35. .
Includes bibliographical references and index.
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.
9783834818447
Geometry, Algebraic
Algebraic topology
Sheaf theory
Riemann surfaces
Surfaces, Riemann
Sheaf cohomology
Sheaves (Algebraic topology)
Algebraische Geometrie
Garbe (Math.)
Homologische Algebra
Kohomologie
Kommutative Algebra
Komplexe Analysis
512.7 / HAR-L
Lectures on algebraic geometry I : sheaves, cohomology of sheaves, and applications to riemann surfaces - 2nd rev ed. - Wiesbaden : Vieweg+Teubner Verlag, 2011. - xiii, 299p. - Aspects of mathematics. E ; v. 35. .
Includes bibliographical references and index.
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.
9783834818447
Geometry, Algebraic
Algebraic topology
Sheaf theory
Riemann surfaces
Surfaces, Riemann
Sheaf cohomology
Sheaves (Algebraic topology)
Algebraische Geometrie
Garbe (Math.)
Homologische Algebra
Kohomologie
Kommutative Algebra
Komplexe Analysis
512.7 / HAR-L
