Moduli spaces of marked branched projective structures on surfaces
Year: 2024
Type: article
Abstract: We show that the moduli space 𝒫 g ( n ) of marked branched projective structures of genus g and branching degree n is a complex analytic space. In the case g ≥ 2 , we show that 𝒫 g ( n ) is of dimension 6 g - 6 + n and we characterize its singular points in terms of their monodromy. We introduce a notion of branching class, that is an infinitesimal description of branched projective structures at the branched points. We show that the space 𝒜 g ( n ) of marked branching classes of genus g and branching degree n is a complex manifold. We show that if n < 2 g - 2 the space 𝒫 g ( n ) is an affine bundle over 𝒜 g ( n ) , while if n > 4 g - 4 , 𝒫 g ( n ) is an analytic subspace of 𝒜 g ( n ) .
DOI: 10.5802/jep.279
Author: Gustave Billon
Institution: Institut de Recherche Mathématique Avancée
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4283324193