The noded Schottky space

Hidalgo, R. A

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).

Más información

Título de la Revista: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
Volumen: 73
Número: 2
Editorial: Wiley
Fecha de publicación: 1996
Página de inicio: 385
Página final: 403
URL: http://www.scopus.com/inward/record.url?eid=2-s2.0-0040688888&partnerID=q2rCbXpz