Abelian automorphisms groups of Schottky type

Rubén A. Hidalgo


We study the problem of lifting an Abelian group H of automorphisms of a closed Riemann surface S (containing anticonformals ones) to a suitable Schottky uniformization of S (that is, when H is of Schottky type). If H+ is the index two subgroup of orientation preserving automorphisms of H and R = S/H+, then H induces an anticonformal automorphism τ : R → R. If τ has fixed points, then we observe that H is of Schottky type. If τ has no fixed points, then we provide a sufficient condition for H to be of Schottky type. We also give partial answers for the excluded cases.

Palabras clave

Automorphisms; Abelian groups; closed Riemann surfaces; automorfismos; grupos abelianos; superficies de Riemann cerradas.

Texto completo:



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DOI: http://dx.doi.org/10.4067/S0716-09172004000300001

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