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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 19, Issue 4


Limit points of the branch locus of đť“śg

Raquel DĂ­az
  • Corresponding author
  • Departamento de GeometrĂ­a y TopologĂ­a, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid, España
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/ Víctor González-Aguilera
Published Online: 2019-06-23 | DOI: https://doi.org/10.1515/advgeom-2018-0029


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


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About the article

Received: 2017-03-19

Revised: 2017-12-28

Published Online: 2019-06-23

Published in Print: 2019-10-25

Communicated by: J. Ratcliffe

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

Citation Information: Advances in Geometry, Volume 19, Issue 4, Pages 505–526, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0029.

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