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.

Full text (pdf)

Opuscula Mathematica - cover

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

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.