Vol. 107, No. 1, 1983

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ISSN: 0030-8730
On the uniformization of certain curves

Peter Frederick Stiller

Vol. 107 (1983), No. 1, 229–244
Abstract

The uniformization theorem of Poincaré and Koebe tells us that every smooth connected algebraic curve X over the complex numbers (or any Riemann surface) has as its universal covering space either the complex projective line PC1, the complex numbers C, or the complex upper half plane H = {z C s.t. Imz > 0}. When the universal covering space is the upper half plane H, we can regard the fundamental group π1(X) as a subgroup of SL2(R) acting as covering transformations via linear fractional transformation. We shall focus on the case π1(X) SL2(Z).

Mathematical Subject Classification 2000
Primary: 14H15
Secondary: 14D05, 30F10
Milestones
Received: 29 January 1981
Revised: 11 January 1982
Published: 1 July 1983
Authors
Peter Frederick Stiller