Symmetries of Compact Riemann Surfaces

ISBN-13: 9783642148279 / Angielski / Miękka / 2010 / 164 str.

Emilio Bujalance;Francisco Javier Cirre;José Manuel Gamboa

Opis

This monograph covers symmetries of compact Riemann surfaces. It examines the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.

Recenzje

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)

Spis treści

Preliminaries.- On the Number of Conjugacy Classes of Symmetries of Riemann Surfaces.- Counting Ovals of Symmetries of Riemann Surfaces.- Symmetry Types of Some Families of Riemann Surfaces.- Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms.

Blurb

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.