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Compact Riemann Surfaces

  • Book
  • © 1992

Overview

Authors:
  1. Raghavan Narasimhan

    1. Department of Mathematics, University of Chicago, Chicago, USA

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Part of the book series: Lectures in Mathematics. ETH Zürich (LM)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-v
    Download chapter PDF

  2. Algebraic functions

    • Raghavan Narasimhan
    Pages 3-7

  3. Riemann Surfaces

    • Raghavan Narasimhan
    Pages 8-11

  4. The Sheaf of Germs of Holomorphic Functions

    • Raghavan Narasimhan
    Pages 12-14

  5. The Riemann Surface of an Algebraic Function

    • Raghavan Narasimhan
    Pages 15-16

  6. Sheaves

    • Raghavan Narasimhan
    Pages 17-26

  7. Vector Bundles, Line Bundles and Divisors

    • Raghavan Narasimhan
    Pages 27-31

  8. Finiteness Theorems

    • Raghavan Narasimhan
    Pages 32-37

  9. The Dolbeault Isomorphism

    • Raghavan Narasimhan
    Pages 38-42

  10. Weyl’s Lemma and the Serre Duality Theorem

    • Raghavan Narasimhan
    Pages 43-48

  11. The Riemann-Roch Theorem and some Applications

    • Raghavan Narasimhan
    Pages 49-57

  12. Further Properties of Compact Riemann Surfaces

    • Raghavan Narasimhan
    Pages 58-62

  13. Hyperelliptic Curves and the Canonical Map

    • Raghavan Narasimhan
    Pages 63-65

  14. Some Geometry of Curves in Projective Space

    • Raghavan Narasimhan
    Pages 66-76

  15. Bilinear Relations

    • Raghavan Narasimhan
    Pages 77-83

  16. The Jacobian and Abel’s Theorem

    • Raghavan Narasimhan
    Pages 84-90

  17. The Riemann Theta Function

    • Raghavan Narasimhan
    Pages 91-96

  18. The Theta Divisor

    • Raghavan Narasimhan
    Pages 97-105

  19. Torelli’s Theorem

    • Raghavan Narasimhan
    Pages 106-110

  20. Riemann’s Theorem on the Singularities of Θ

    • Raghavan Narasimhan
    Pages 111-118
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Keywords

Authors and Affiliations

  • Department of Mathematics, University of Chicago, Chicago, USA

    Raghavan Narasimhan

Bibliographic Information

  • Book Title: Compact Riemann Surfaces

  • Authors: Raghavan Narasimhan

  • Series Title: Lectures in Mathematics. ETH Zürich

  • DOI: https://doi.org/10.1007/978-3-0348-8617-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1992

  • Softcover ISBN: 978-3-7643-2742-2Published: 01 September 1992

  • eBook ISBN: 978-3-0348-8617-8Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VI, 122

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Analysis

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