On triangular (D_{n})-actions on cyclic p-gonal Riemann surfaces

Opuscula Mathematica

Ewa Tyszkowska¹ 

[1] University of Gdańsk, Institute of Mathematics, Wita Stwosza 57, 80-952 Gdańsk, Poland;

关键词: Riemann surface;    symmetry;    triangle group;    Fuchsian group;    NEC group;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2016.36.1.103

来源: DOAJ

【 摘 要 】

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 \(D_n\).

【 授权许可】

Unknown