Riemann Surfaces
Simon Donaldson
24 March 2011
ISBN: 9780199606740
304 pages
Paperback
234x156mm
In Stock
Oxford Graduate Texts in Mathematics
Price: £40.99An 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.
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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