Klein's curve
Abstract
Riemann surfaces with symmetries arise in many studies of integrable systems. We illustrate new techniques in investigating such surfaces by means of an example. By giving a homology basis well adapted to the symmetries of Klein's curve, presented as a plane curve, we derive a new expression for its period matrix. This is explicitly related to the hyperbolic model and results of Rauch and Lewittes.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2010
 DOI:
 10.1088/17518113/43/43/434009
 arXiv:
 arXiv:0905.4202
 Bibcode:
 2010JPhA...43Q4009B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematical Physics;
 Mathematics  Representation Theory
 EPrint:
 16 pages 5 figures. Final version makes connection with other known period matrices