Lectures on Algebraic Geometry I

Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces
2. überarbeitete Auflage 2011
ISBN: 978-3-8348-1844-7
Verlag: Springer

Buch, Englisch, 301 Seiten, Format (B × H): 173 mm x 246 mm, Gewicht: 773 g

Reihe: Aspects of Mathematics

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.

Zielgruppe

Mathematiker und Studierende höherer Semester, die sich für algebraische Geometrie und deren Beziehungen zur Topologie und zur Zahlentheorie in der Forschung interessieren

Autoren/Hrsg.

Harder, Günter

Weitere Mitwirkende

Diederich, Klas

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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

Über Autor(innen)

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