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Preprints, Working Papers, ... Year : 2023

Branched Projective Structures and Bundles of Projective Frames on Surfaces

Gustave Billon

Abstract

We show that the description of the holomorphic projective 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 projective bundle, and is consequently an affine space. Finally, we study the map which to a branching class associates the corresponding projective bundle with section.
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hal-04246665 , version 1 (17-10-2023)

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Gustave Billon. Branched Projective Structures and Bundles of Projective Frames on Surfaces. 2023. ⟨hal-04246665⟩

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