Lectures on Algebraic Geometry I (eBook)

Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces

Günter Harder (Autor)

eBook Download: PDF

2011 | 2nd ed. 2011
XIII, 301 Seiten
Springer Fachmedien Wiesbaden GmbH (Verlag)
978-3-8348-8330-8 (ISBN)

Infos

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.


Prof. Dr. Günter Harder, Max-Planck-Institute for Mathematics, Bonn

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 15.9.2011
• Reihe/Serie: Aspects of Mathematics
• Reihe/Serie: Aspects of Mathematics
• Mitarbeit: Herausgeber (Serie): Klas Diederich
• Zusatzinfo: XIII, 301 p.
• Verlagsort: Wiesbaden
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• Schlagworte: Algebraische Geometrie • Garbe (Math.) • Homologische Algebra • Kohomologie • Kommutative Algebra • Komplexe Analysis
• ISBN-10: 3-8348-8330-1 / 3834883301
• ISBN-13: 978-3-8348-8330-8 / 9783834883308