On the connectedness of the branch locus of the moduli space of Riemann surfaces

  • Gabriel Bartolini
  • Antonio F. Costa
  • Milagros Izquierdo
  • Ana M. Porto
Article

Abstract

The moduli space \( \mathcal{M}_g \) of compact Riemann surfaces of genus g has the structure of an orbifold and the set of singular points of such orbifold is the branch locus\( \mathcal{B}_g \). In this article we present some results related with the topology of \( \mathcal{B}_g \). We study the connectedness of \( \mathcal{B}_g \) for g ≤ 8, the existence of isolated equisymmetric strata in the branch loci and finally we stablish the connectedness of the branch locus of the moduli space of Riemann surfaces consIDered as Klein surfaces. We just sketch the proof of some of the results; complete proofs will be published elsewhere.

Keywords

Riemann surface moduli space automorphism 

Mathematics Subject Classifications

32G15 14H15 

Sobre la conexión del conjunto singular del espacio de moduli de las surperficies de Riemann

Resumen

El espacio de moduli \( \mathcal{M}_g \) de las superficies de Riemann de género g tiene estructura de orbifold y el conjunto de puntos singulares de tal orbifold es el conjunto singular \( \mathcal{B}_g \). En este artículo presentamos algunos resultados acerca de la topologyía de \( \mathcal{B}_g \). Concretamente se estudia la conexión de \( \mathcal{B}_g \) para g ≤ 8, la existencia de estratos equisimétricos aislados de ciertas dimensiones en \( \mathcal{B}_g \) y finalmente se establece la conexión del conjunto singular del espacio de moduli de las superficies de Riemann consIDeradas como superficies de Klein.

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Copyright information

© Springer 2010

Authors and Affiliations

  • Gabriel Bartolini
    • 1
  • Antonio F. Costa
    • 2
  • Milagros Izquierdo
    • 1
  • Ana M. Porto
    • 2
  1. 1.Matematiska InstitutionenLinköpings UniversitetLinköpingSweden
  2. 2.Departamento de Matemáticas Fundamentales Facultad de CienciasUNEDMadrIDSpain

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