On the uniformization of certain curves
Academic Article

Overview

Identity

Additional Document Info

View All

Overview

abstract

The uniformization theorem of Poincar 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 S = {z C s.t. Im z > 0}. When the universal covering space is the upper half plane S, we can regard the fundamental group 1(X) as a subgroup of SL2(R) acting as covering transformations via linear fractional transformation. We shall focus on the case 1(X) SL2(Z). 1983 by Pacific Journal of Mathematics.