Riemann and Klein Surfaces with Nodes Viewed as Quotients

Abstract

If G is a group of automorphisms that acts properly discontinuously on a Riemann or Klein surface X, then there exists a unique structure of Riemann or Klein surface on X/G such that the projection π : X → X/G is a morphism. The analogous result is not true when we deal with surfaces with nodes. In this paper we give a new definition of a group that acts properly discontinuously on a surface with nodes in order to obtain a similar theorem.