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arXiv · 2310.09037

Branched Projective Structures and Bundles of Projective Frames on Surfaces

Gustave Billon
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Abstract

We show that the description of the holomorphic $\mathbb C \mathrm P^1$-bundle associated to a holomorphic projective structure on a Riemann surface in terms of the principal bundle of projective $2$-frames extends very well to the setting of branched projective structures. This generalization reveals a space of parameters, each of which is associated to a branching class. The space of branched projective structures with a given branching class appears as a space of connections on a given $\mathbb C \mathrm P^1$-bundle, and is consequently an affine space. Finally, we study the map which to a branching class associates the corresponding $\mathbb C \mathrm P^1$-bundle with section.

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Gustave Billon. 2023-10-13. Branched Projective Structures and Bundles of Projective Frames on Surfaces. https://arxiv.org/abs/2310.09037

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