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Lectures on Algebraic Geometry I

Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces

von Harder, Günter   (Autor)

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.

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Produktbeschreibung

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. 

Inhaltsverzeichnis

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

Kritik

"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 

Autoreninfo

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

Mehr vom Verlag:

k.A.

Mehr aus der Reihe:

Mehr vom Autor:

Harder, Günter

Produktdetails

Medium: Buch
Format: Gebunden
Seiten: 316
Sprache: Englisch
Erschienen: September 2011
Auflage: Second überarb. Edition 2011
Band-Nr.: Vol.1
Maße: 246 x 173 mm
Gewicht: 773 g
ISBN-10: 3834818445
ISBN-13: 9783834818447
Verlagsbestell-Nr.: 85048888

Bestell-Nr.: 10812850 
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Libri-Relevanz: 0 (max 9.999)
Bestell-Nr. Verlag: 85048888

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KNO-SAMMLUNG: Aspects of Mathematics 35
KNOABBVERMERK: 2nd, rev. ed. 2012. xiii, 301 S. XIII, 301 p. 240 mm
KNOMITARBEITER: Herausgegeben:Diederich, Klas
KNO-BandNr. Text:Vol.1
Einband: Gebunden
Auflage: Second überarb. Edition 2011
Sprache: Englisch
Beilage(n): HC runder Rücken kaschiert

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