Spherical conic metrics and realizability of branched covers
Geometric Topology
2020-09-02 v3 Differential Geometry
Abstract
Branched covers between Riemann surfaces are associated with certain combinatorial data, and Hurwitz existence problem asks whether given data satisfying those combinatorial constraints can be realized by some branched cover. We connect recent development in spherical conic metrics to this old problem, and give a new method of finding exceptional (unrealizable) branching data. As an application, we find new infinite sets of exceptional branched cover data on the Riemann sphere.
Keywords
Cite
@article{arxiv.1805.03312,
title = {Spherical conic metrics and realizability of branched covers},
author = {Xuwen Zhu},
journal= {arXiv preprint arXiv:1805.03312},
year = {2020}
}
Comments
15 pages, 3 figures. To appear in Proceedings of the AMS