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Riemann Surfaces

Simon Donaldson

24 March 2011

ISBN: 9780199606740

304 pages
Paperback
234x156mm

In Stock

Oxford Graduate Texts in Mathematics

Price: £40.99

An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

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Description

An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

  • Established author with an international research reputation
  • The topic stands at the centre of a number of key areas
  • Novel, innovative approach to the fundamental results
  • Emphasis on topology and the interaction with global analysis

About the Author(s)

Simon Donaldson, Royal Society Research Professor, Imperial College, London

Table of Contents

    I Preliminaries
    1:Holomorphic Functions
    2:Surface Topology
    II Basic Theory
    3:Basic Definitions
    4:Maps between Riemann Surfaces
    5:Calculus on Surfaces
    6:Elliptic functions and integrals
    7:Applications of the Euler characteristic
    III Deeper Theory
    8:Meromorphic Functions and the Main Theorem for Compact Riemann Surfaces
    9:Proof of the Main Theorem
    10:The Uniformisation Theorem
    IV Further Developments
    11:Contrasts in Riemann Surface Theory
    12:Divisors, Line Bundles and Jacobians
    13:Moduli and Deformations
    14:Mappings and Moduli
    15:Ordinary Differential Equations
    Bibliography
    Index

Reviews

"This clear and insightful text, from one of the foremost researchers in the field, is suitable for graduate or advanced undergraduate course on Riemann surfaces, and will provide fascinating reading for professional mathematicians." - L'Enseignement Mathematique

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