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Schottky uniformizations of closed Riemann surfaces with Abelian groups of conformal automorphisms

Published online by Cambridge University Press:  18 May 2009

Rubén A. Hidalgo
Rubén A. Hidalgo
Affiliation:
Departamento de Mathemáticas, UTFSM, Valparaiso, Chile
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Let us consider a pair (S, H) consisting of a closed Riemann surface S and an Abelian group H of conformal automorphisms of S. We are interested in finding uniformizations of S, via Schottky groups, which reflect the action of the group H. A Schottky uniformization of a closed Riemann surface S is a triple (Ώ, G, π:Ώ→S) where G is a Schottky group with Ώ as its region ofdiscontinuity and π:Ώ→S is a holomorphic covering with G ascovering group. We look for a Schottky uniformization (Ώ, G, π:Ώ→S) of S such that for each transformation h in H there exists an automorphisms t of Ώ satisfying h ∘ π = π ∘ t.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 17 - 32
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

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