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.
Author(s): Emilio Bujalance, Francisco Javier Cirre, José Manuel Gamboa, Grzegorz Gromadzki (auth.)
Series: Lecture Notes in Mathematics 2007
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2010
Language: English
Pages: 164
Tags: Functions of a Complex Variable; Algebraic Geometry; Group Theory and Generalizations; Topology
Front Matter....Pages i-xx
Preliminaries....Pages 1-20
On the Number of Conjugacy Classes of Symmetries of Riemann Surfaces....Pages 21-32
Counting Ovals of Symmetries of Riemann Surfaces....Pages 33-63
Symmetry Types of Some Families of Riemann Surfaces....Pages 65-90
Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms....Pages 91-143
Appendix....Pages 145-149
Back Matter....Pages 151-158
