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arXiv · 2105.07084

Monodromies of Projective Structures on Surface of Finite-type

Genyle Nascimento
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Abstract

We characterize the monodromies of projective structures with fuchsian-type singularities. Namely, any representation from the fundamental group of a Riemann surface of finite-type in $PSL_2(\mathbb{C})$ can be represented as the holonomy of branched projective structure with fuchsian-type singularities over the cusps. We made a geometrical/topological study of all local conical projective structures whose Schwarzian derivative admits a simple pole at the cusp. Finally, we explore isomonodromic deformations of such projective structures and the problem of minimizing angles.

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Genyle Nascimento. 2021-05-14. Monodromies of Projective Structures on Surface of Finite-type. https://arxiv.org/abs/2105.07084

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