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  • Book
  • © 1992

Compact Riemann Surfaces

Birkhäuser

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

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  • ISBN: 978-3-0348-8617-8
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Table of contents (19 chapters)

  1. Front Matter

    Pages i-v
  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

Keywords

  • Finite
  • Fundamental theorem of calculus
  • Morphism
  • algebra
  • differential equation
  • function
  • geometry
  • mathematics
  • proof
  • theorem

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: 978-3-7643-2742-2

  • eBook ISBN: 978-3-0348-8617-8

  • Edition Number: 1

  • Number of Pages: VI, 122

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Analysis

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-3-0348-8617-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 69.99
Price excludes VAT (USA)