Opuscula Math. 36, no. 1 (2016), 103-122

Opuscula Mathematica

On triangular (Dn)-actions on cyclic p-gonal Riemann surfaces

Ewa Tyszkowska

Abstract. A compact Riemann surface \(X\) of genus \(g\gt 1\) which has a conformal automorphism \(\rho\) of prime order \(p\) such that the orbit space \(X/ \langle \rho \rangle \) is the Riemann sphere is called cyclic \(p\)-gonal. Exceptional points in the moduli space \(\mathcal{M}_g\) of compact Riemann surfaces of genus \(g\) are unique surface classes whose full group of conformal automorphisms acts with a triangular signature. We study symmetries of exceptional points in the cyclic \(p\)-gonal locus in \(\mathcal{M}_g\) for which \(\text{Aut}(X)/ \langle \rho \rangle\) is a dihedral group \(D_n\).

Keywords: Riemann surface, symmetry, triangle group, Fuchsian group, NEC group.

Mathematics Subject Classification: 30F10, 14H37.

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  • Ewa Tyszkowska
  • University of Gdańsk, Institute of Mathematics, Wita Stwosza 57, 80-952 Gdańsk, Poland
  • Communicated by P.A. Cojuhari.
  • Received: 2014-11-11.
  • Revised: 2015-02-16.
  • Accepted: 2015-02-17.
  • Published online: 2015-09-19.
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Cite this article as:
Ewa Tyszkowska, On triangular (Dn)-actions on cyclic p-gonal Riemann surfaces, Opuscula Math. 36, no. 1 (2016), 103-122, http://dx.doi.org/10.7494/OpMath.2016.36.1.103

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