Schottky Uniformizations of Z22 Actions on Riemann Surfaces

Abstract

Given a closed Riemann surface S together a group of its conformal automorphisms H ∼ = Z 2 2 , it is known that there are Schottky uniformizations of S realizing H. In this note we proceed to give an explicit Schottky uniformizations for each of all different topological actions of Z 2 2 as group of conformal automorphisms on a closed Riemann surface.