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Geometry of the 1-skeleta of singular nerves of moduli spaces of Riemann surfaces

Original Paper
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Abstract

Cornalba (Ann Mat Pura Appl 149:135–151, 1987) classified the components of the singular locus of the moduli space of compact Riemann surfaces of genus \(g \ge 2\). Here we consider the problem of describing the intersections of these components by examining certain nerves of the cover of singular locus that the Cornalba components provide. We give a description of the 1-skeleton of such nerves which significantly extends the results of our earlier paper written together with A. Weaver where we considered a coarser cover of the singular locus. We compare the results of our earlier work with those of the present one in terms of certain natural simplicial covering maps between them.

Keywords

Riemann surface Moduli space of Riemann surfaces Singular locus Automorphisms of Riemann surface Fuchsian groups Riemann uniformization theorem 

Mathematics Subject Classification

Primary 30F 14H Secondary 20F 

Notes

Acknowledgements

The authors are very gratefull to each of both referees for their valuable comments and suggestions which allowed us to avoid some imprecisions and omissions.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics, Physics and Informatics, Institute of MathematicsUniversity of GdańskGdańskPoland
  2. 2.Department of MathematicsUniversity of PortlandPortlandUSA

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