Moduli spaces of marked branched projective structures on surfaces
type: Item
instance of: scholarly article
title: Moduli spaces of marked branched projective structures on surfaces
author: Gustave Billon
publication date: 2024-11-12T00:00:00Z
review text: Let \(\mathcal P_g(n)\) be the moduli spaces of marked branched projective structures of genus \(g\) and branching degree \(n\). The author proves that \(\mathcal P_g(n)\) is a complex analytic space of dimension \(6g-6+n\) and if \(g\geq 2\) its singular points are characterized in terms of their monodromy.\N\NThe author also introduces the notions of branching class and shows that the moduli space \(\mathcal A_g(n)\) of marked branching classes of genus \(g\) and branching degree \(n\) is a complex manifold. Furthermore, the author proves that \(\mathcal P_g(n)\) is an affine bundle over \(\mathcal A_g(n)\) if \(n<2g-2\) and that \(\mathcal P_g(n)\) is an analytic subspace of \(\mathcal A_g(n)\) if \(n>4g-4.\)
reviewed by: Angelina Zheng
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 14H15
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 7942489
zbMATH Keywords: complex projective structures
zbMATH Keywords: moduli spaces
zbMATH Keywords: families of Riemann surfaces
MaRDI profile type: Publication
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published in: Journal de l’École polytechnique — Mathématiques
DOI: 10.5802/JEP.279
description: scientific article; zbMATH DE number 7942489