The monodromy groups of Schwarzian equations on closed Riemann surfaces
Complex Variables
2009-09-25 v2
Abstract
Let \theta:\pi_1(R) \to \PSL(2,\C) be a homomorphism of the fundamental group of an oriented, closed surface R of genus exceeding one. We will establish the following theorem. Theorem. Necessary and sufficient for \theta to be the monodromy representation associated with a complex projective stucture on R, either unbranched or with a single branch point of order 2, is that \theta(\pi_1(R)) be nonelementary. A branch point is required if and only if the representation \theta does not lift to \SL(2,\C).
Keywords
Cite
@article{arxiv.math/9511213,
title = {The monodromy groups of Schwarzian equations on closed Riemann surfaces},
author = {Daniel Gallo and Michael Kapovich and Albert Marden},
journal= {arXiv preprint arXiv:math/9511213},
year = {2009}
}
Comments
80 pages, published version