Computation of highly ramified coverings
Algebraic Geometry
2013-10-04 v1 Classical Analysis and ODEs
Abstract
An almost Belyi covering is an algebraic covering of the projective line, such that all ramified points except one simple ramified point lie above a set of 3 points of the projective line. In general, there are 1-dimensional families of these coverings with a fixed ramification pattern. (That is, Hurwitz spaces for these coverings are curves.) In this paper, three almost Belyi coverings of degrees 11, 12, and 20 are explicitly constructed. We demonstrate how these coverings can be used for computation of several algebraic solutions of the sixth Painleve equation.
Keywords
Cite
@article{arxiv.0705.3134,
title = {Computation of highly ramified coverings},
author = {Raimundas Vidunas and Alexander Kitaev},
journal= {arXiv preprint arXiv:0705.3134},
year = {2013}
}
Comments
26 pages