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Lectures on Algebraic Geometry II

Basic Concepts, Coherent Cohomology, Curves and their Jacobians

  • Book
  • © 2011

Overview

Authors:
  1. Günter Harder

    1. Max-Planck-Institute for Mathematics, Bonn, Germany

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  • Algebraische Geometrie:
  • Von Abel und Riemann

Part of the book series: Aspects of Mathematics (ASMA)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Basic Concepts of the Theory of Schemes

    • Günter Harder
    Pages 1-53

  3. Some Commutative Algebra

    • Günter Harder
    Pages 55-119

  4. Projective Schemes

    • Günter Harder
    Pages 121-182

  5. Curves and the Theorem of Riemann-Roch

    • Günter Harder
    Pages 183-264

  6. The Picard functor for curves and their Jacobians

    • Günter Harder
    Pages 265-356

  7. Back Matter

    Pages 357-365
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Keywords

About this book

In this second volume of "Lectures on Algebraic Geometry", the author starts with some foundational concepts in the theory of schemes and gives a somewhat casual introduction into commutative algebra. After that he proves the finiteness results for coherent cohomology and discusses important applications of these finiteness results. In the two last chapters, curves and their Jacobians are treated and some outlook into further directions of research is given.
The first volume is not necessarily a prerequisite for the second volume if the reader accepts the concepts on sheaf cohomology. On the other hand, the concepts and results in the second volume have been historically inspired by the theory of Riemann surfaces. There is a deep connection between these two volumes, in spirit they form a unity.


Basic concepts of the Theory of Schemes - Some Commutative Algebra - Projective Schemes - Curves and the Theorem of Riemann-Roch - The Picard functor for curves and Jacobians.

Prof. Dr. Günter Harder, Department of Mathematics, University of Bonn, and Max-Planck-Institute for Mathematics, Bonn, Germany.

Authors and Affiliations

  • Max-Planck-Institute for Mathematics, Bonn, Germany

    Günter Harder

About the author

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

Bibliographic Information

  • Book Title: Lectures on Algebraic Geometry II

  • Book Subtitle: Basic Concepts, Coherent Cohomology, Curves and their Jacobians

  • Authors: Günter Harder

  • Series Title: Aspects of Mathematics

  • DOI: https://doi.org/10.1007/978-3-8348-8159-5

  • Publisher: Vieweg+Teubner Verlag Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2011

  • Hardcover ISBN: 978-3-8348-0432-7Published: 05 April 2011

  • Softcover ISBN: 978-3-8348-2686-2Published: 12 October 2014

  • eBook ISBN: 978-3-8348-8159-5Published: 21 April 2011

  • Series ISSN: 0179-2156

  • Edition Number: 1

  • Number of Pages: XIII, 365

  • Topics: Algebraic Geometry, Algebra

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