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March 23, 2026Advances in Geometry

Boundary of equisymmetric loci of Riemann surfaces with abelian symmetry

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Authors

RDRaquel DíazVGVíctor González-Aguilera

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Overview

This work uncovers topological types of maximal dimension strata in Riemann surfaces, indicating connections to automorphism groups.

Key Points

  • To determine the topological type of maximal dimension strata at the boundary of equisymmetric loci in the moduli space of Riemann surfaces.
  • Examined the moduli space of Riemann surfaces of genus g ≥ 2
  • Analyzed equisymmetric loci related to abelian automorphism groups
  • Described topological strata in specific cases of hyperelliptic and cyclic p-gonal actions
  • Identified the structure of maximal dimension strata at their boundary
  • Described topological strata in terms of trees with a fixed number of edges

Cite This Study

Díaz et al. (2026) studied this question.

synapsesocial.com/papers/69c08b86a48f6b84677f8fdbhttps://doi.org/10.1515/advgeom-2026-0009
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