Opuscula Math. 36, no. 1 (2016), 103-122
http://dx.doi.org/10.7494/OpMath.2016.36.1.103
Opuscula Mathematica
On triangular (Dn)-actions on cyclic p-gonal Riemann surfaces
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.
