Boundary of equisymmetric loci of Riemann surfaces with abelian symmetry

2024/11/14 by Raquel Díaz, Víctor González-Aguilera, Díaz, Raquel +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Primary 32G15 #Secondary 14H10

paper · pdf · doi:10.48550/arxiv.2411.09836

openalex publication_date 2024/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathcal M_g be the moduli space of compact connected Riemann surfaces of genus g≥ 2 and let \widehat\mathcal M_g be its Deligne-Mumford compactification, which is stratified by the topological type of the stable Riemann surfaces. We consider the equisymmetric loci in \mathcal M_g corresponding to Riemann surfaces whose automorphism group is abelian and determine the topological type of the maximal dimension strata at their boundary. For the particular cases of the hyperelliptic and the cyclic p-gonal actions, we describe all the topological strata at the boundary in terms of trees with a fixed number of edges.

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