Abstract

We introduce coordinates, given by fixed points, for the marked Schottky space Sg of genus g ? 2. With these coordinates, different to the ones given by Bers, Sato and Gerritzen, we can think of the space Sg as an open subset of ?? × ?3g-4. A partial closure of Sg, denoted by NSg and called the marked noded Schottky space of genus g, is considered. Each point in NSg corresponds to a geometrically finite free group of rank g, called a (marked) noded Schottky group of genus g. Conversely, each such group corresponds to a point in NSg. We have that each noded Schottky group of genus g uniformizes a stable Riemann surface of genus g. Moreover, we show that every stable Riemann surface is uniformized by such a group (retrosection theorem with nodes).