On the existence of connected components of dimension one in the branch locus of moduli spaces of Riemann surfaces

• Autores: Antonio Félix Costa González, Milagros Izquierdo Barrios
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 111, Nº 1, 2012, págs. 53-64
• Idioma: inglés
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• Resumen

  • Let g be an integer ≥3 and let Bg={X∈Mg:Aut(X)≠Id} be the branch locus of Mg, where Mg denotes the moduli space of compact Riemann surfaces of genus g. The structure of Bg is of substantial interest because Bg corresponds to the singularities of the action of the modular group on the Teichmüller space of surfaces of genus g (see [14]). Kulkarni ([15], see also [13]) proved the existence of isolated points in the branch loci of the moduli spaces of Riemann surfaces. In this work we study the isolated connected components of dimension 1 in such loci. These isolated components of dimension one appear if the genus is g=p−1 with p prime ≥11. We use uniformization by Fuchsian groups and the equisymmetric stratification of the branch loci.