On the uniformization of certain curves Academic Article uri icon

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.
  • 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 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 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). © 1983 by Pacific Journal of Mathematics.

published proceedings

  • Pacific Journal of Mathematics

author list (cited authors)

  • Stiller, P.

citation count

  • 2

complete list of authors

  • Stiller, Peter

publication date

  • July 1983