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Symmetries of Compact Riemann Surfaces

  • Book
  • © 2010

Overview

Authors:
  1. Emilio Bujalance

    1. Matemáticas Fundamentales, Facultad de Ciencias, UNED, Madrid, Spain

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  2. Francisco Javier Cirre

    1. Matemáticas Fundamentales, Facultad de Ciencias, UNED, Madrid, Spain

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  3. José Manuel Gamboa

    1. Facultad de Matemáticas, UCM, Departamento de Álgebra, Universidad Complutense Madrid, Madrid, Spain

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  4. Grzegorz Gromadzki

    1. Department of Mathematics, University of Gdansk, Gdansk, Poland

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  • The monograph deals with topics of increasing research interest nowadays.
  • Suitable for graduate level.
  • Numerous results scattered across the literature are collected together.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2007)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xx
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  2. Preliminaries

    • Emilio Bujalance, Francisco Javier Cirre, José Manuel Gamboa, Grzegorz Gromadzki
    Pages 1-20

  3. On the Number of Conjugacy Classes of Symmetries of Riemann Surfaces

    • Emilio Bujalance, Francisco Javier Cirre, José Manuel Gamboa, Grzegorz Gromadzki
    Pages 21-32

  4. Counting Ovals of Symmetries of Riemann Surfaces

    • Emilio Bujalance, Francisco Javier Cirre, José Manuel Gamboa, Grzegorz Gromadzki
    Pages 33-63

  5. Symmetry Types of Some Families of Riemann Surfaces

    • Emilio Bujalance, Francisco Javier Cirre, José Manuel Gamboa, Grzegorz Gromadzki
    Pages 65-90

  6. Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms

    • Emilio Bujalance, Francisco Javier Cirre, José Manuel Gamboa, Grzegorz Gromadzki
    Pages 91-143

  7. Appendix

    • Emilio Bujalance, Francisco Javier Cirre, José Manuel Gamboa, Grzegorz Gromadzki
    Pages 145-149

  8. Back Matter

    Pages 151-158
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Keywords

About this book

This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.

Reviews

From the reviews:

“The monograph under review is primarily a survey of recent advances in the theory of symmetries of compact Riemann surfaces. It also provides a number of new interesting developments and different methods of proof for some of the recent and classical results in this area as well as a number of illustrative and detailed examples highlighting these results. With its informative and well-written introduction and a substantial preliminaries section, this monograph is ideal for both beginners to the area and current researchers.” (Aaron D. Wootton, Mathematical Reviews, Issue 2011 h)

Authors and Affiliations

  • Matemáticas Fundamentales, Facultad de Ciencias, UNED, Madrid, Spain

    Emilio Bujalance, Francisco Javier Cirre

  • Facultad de Matemáticas, UCM, Departamento de Álgebra, Universidad Complutense Madrid, Madrid, Spain

    José Manuel Gamboa

  • Department of Mathematics, University of Gdansk, Gdansk, Poland

    Grzegorz Gromadzki

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