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

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.
• Revised: 2015-02-16.
• Accepted: 2015-02-17.
• Published online: 2015-09-19.