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Limit points of the branch locus of đť“śg

  • Raquel DĂ­az EMAIL logo and VĂ­ctor González-Aguilera
Published/Copyright: June 23, 2019
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Advances in Geometry
From the journal Advances in Geometry Volume 19 Issue 4

Abstract

Let 𝓜g be the moduli space of compact connected hyperbolic surfaces of genus g ≥ 2, and 𝓑g ⊂ 𝓜g its branch locus. Let Mg^ be the Deligne–Mumford compactification of the moduli space of smooth, complete, connected surfaces of genus g ≥ 2 over ℂ. The branch locus 𝓑g is stratified by smooth locally closed equisymmetric strata, where a stratum consists of hyperbolic surfaces with equivalent action of their orientation-preserving isometry group. Any stratum can be determined by a certain epimorphism Φ. In this paper, for any of these strata, we describe the topological type of its limits points in 𝓜͡g in terms of Φ. We apply our method to the 2-complex dimensional stratum corresponding to the pyramidal hyperbolic surfaces.

Keywords: Moduli space; stratification; noded Riemann surfaces
MSC 2010: Primary 32G15; Secondary 14H10

  1. Communicated by: J. Ratcliffe

  2. Funding: The first author was partially supported by the Project MTM2012-31973. The second author was partially supported by Project PIA, ACT 1415.

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Received: 2017-03-19
Revised: 2017-12-28
Published Online: 2019-06-23
Published in Print: 2019-10-25

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. A Batyrev type classification of â„š-factorial projective toric varieties
  3. Blocking sets of certain line sets related to a hyperbolic quadric in PG(3, q)
  4. Affine-compact functors
  5. Limit points of the branch locus of đť“śg
  6. Criteria for strict monotonicity of the mixed volume of convex polytopes
  7. Principal curvatures and parallel surfaces of wave fronts
  8. Nodal curves with a contact-conic and Zariski pairs
  9. Corrigendum to the paper “On surfaces with two apparent double points”
https://doi.org/10.1515/advgeom-2018-0029
Keywords for this article
Moduli space; stratification; noded Riemann surfaces

Articles in the same Issue

  1. Frontmatter
  2. A Batyrev type classification of â„š-factorial projective toric varieties
  3. Blocking sets of certain line sets related to a hyperbolic quadric in PG(3, q)
  4. Affine-compact functors
  5. Limit points of the branch locus of đť“śg
  6. Criteria for strict monotonicity of the mixed volume of convex polytopes
  7. Principal curvatures and parallel surfaces of wave fronts
  8. Nodal curves with a contact-conic and Zariski pairs
  9. Corrigendum to the paper “On surfaces with two apparent double points”
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