On the existence of connected components of dimension one in the branch locus of moduli spaces of riemann surfaces - Costa, Antonio F.; Izquierdo, Milagros (Mathematica Scandinavica, 2012)
Let g be an integer ≥3 and let B_g={XM_g: Aut(X) eq Id} be the branch locus of M_g, where M_g denotes the moduli space of compact Riemann surfaces of genus g. The structure of B_g is of substantial interest because B_g 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.