English

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 PGL2(C)\mathrm{PGL}_2(\mathbb{C}) 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.

Keywords

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

R2 v1 2026-06-23T00:14:44.986Z