The monodromy of meromorphic projective structures

Dylan G. L. Allegretti; Tom Bridgeland

doi:10.1090/tran/8093

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arXiv · 1802.02505

The monodromy of meromorphic projective structures

Dylan G. L. Allegretti·Tom Bridgeland

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

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Dylan G. L. Allegretti, Tom Bridgeland. 2018-02-07. The monodromy of meromorphic projective structures. https://doi.org/10.1090/tran/8093

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