Topological classification of conformal actions on cyclic p-gonal Riemann surfaces

Topological Classification of Conformal Actions on pq-Hyperelliptic Riemann Surfaces

A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ρ for which X/ρ is an orbifold of genus p. Here we classify conformal actions on 2-hyperelliptic Rieman surfaces of genus g > 9, up to topological conjugacy and determine which of them can be maximal.

On automorphisms groups of cyclic p-gonal Riemann surfaces

In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p ≥ 3 is a prime integer and the genus of the surfaces is at least (p − 1) + 1. We use Fuchsian and NEC groups, and cohomology of finite groups.

SYMMETRIES OF REAL CYCLIC p-GONAL RIEMANN SURFACES

A closed Riemann surface X which can be realised as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. A p-gonal Riemann surface is called real p-gonal if there is an anticonformal involution (symmetry) σ of X commuting with the p-gonal morphism. If the p-gonal morphism is a cyclic regular covering the Riemann surface is called real c...

Research Article Topological Classification of Conformal Actions on pq-Hyperelliptic Riemann Surfaces

On p-hyperelliptic Involutions of Riemann Surfaces

A compact Riemann surface X of genus g > 1 is said to be phyperelliptic if X admits a conformal involution ρ, called a p-hyperelliptic involution, for which X/ρ is an orbifold of genus p. Here we give a new proof of the well known fact that for g > 4p + 1, ρ is unique and central in the group of all automorphisms of X. Moreover we prove that every two p-hyperelliptic involutions commute for 3p ...