Geodesic
Schottky uniformizations of closed Riemann surfaces with Abelian groups of conformal automorphisms
Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 17-32

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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. 
Hidalgo, Rubén A. Schottky uniformizations of closed Riemann surfaces with Abelian groups of conformal automorphisms. Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 17-32. doi: 10.1017/S0017089500030500
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