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  • 1.
    Costa, Antonio F.
    et al.
    Departamento de Matematicas Fundamentales, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Porto, Ana M.
    Departamento de Matematicas Fundamentales, UNED.
    On the connectedness of the branch loci of moduli spaces of orientable Klein surfaces2015In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 177, no 1, p. 149-164Article in journal (Refereed)
    Abstract [en]

    Let M K (g,+,k) be the moduli space of orientable Klein surfaces of genus g with k boundary components (see Alling and Greenleaf in Lecture notes in mathematics, vol 219. Springer, Berlin, 1971; Natanzon in Russ Math Surv 45(6):53–108, 1990). The space M K (g,+,k) has a natural orbifold structure with singular locus B K (g,+,k) . If g>2 or k>0 and 2g+k>3 the set B K (g,+,k) consists of the Klein surfaces admitting non-trivial symmetries and we prove that, in this case, the singular locus is connected.

  • 2.
    Costa, Antonio F.
    et al.
    Departamento de Matematicas Fundamentales, UNED.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Ying, Daniel
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On cyclic p-gonal Riemann surfaces with several p-gonal morphisms2010In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 147, no 1, p. 139-147Article in journal (Refereed)
    Abstract [en]

    Let p be a prime number, p > 2. A closed Riemann surface which can be realized as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. If the p-gonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic p-gonal Riemann surface. Accola showed that if the genus is greater than (p − 1)2 the p-gonal morphism is unique. Using the characterization of p-gonality by means of Fuchsian groups we show that there exists a uniparametric family of cyclic p-gonal Riemann surfaces of genus (p − 1)2 which admit two p-gonal morphisms. In this work we show that these uniparametric families are connected spaces and that each of them is the Riemann sphere without three points. We study the Hurwitz space of pairs (X, f), where X is a Riemann surface in one of the above families and f is a p-gonal morphism, and we obtain that each of these Hurwitz spaces is a Riemann sphere without four points.

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