The monodromy of meromorphic projective structures
Geometric Topology
2020-07-14 v2 Algebraic Geometry
Differential Geometry
Abstract
We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed local systems on the associated marked bordered surface. We prove that the image of this map is contained in the union of the domains of the cluster charts. We discuss a number of open questions concerning this monodromy map.
Cite
@article{arxiv.1802.02505,
title = {The monodromy of meromorphic projective structures},
author = {Dylan G. L. Allegretti and Tom Bridgeland},
journal= {arXiv preprint arXiv:1802.02505},
year = {2020}
}
Comments
54 pages. Version 2: Incorporated suggestions from referee