Abelian automorphisms groups of Schottky type

  • Rubén A. Hidalgo Universidad Técnica Federico Santa María.
Palabras clave: Automorphisms, Abelian groups, closed Riemann surfaces, automorfismos, grupos abelianos, superficies de Riemann cerradas.

Resumen

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.

Biografía del autor/a

Rubén A. Hidalgo, Universidad Técnica Federico Santa María.
Departamento de Matemática.

Citas

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Publicado
2017-05-22
Cómo citar
Hidalgo, R. (2017). Abelian automorphisms groups of Schottky type. Proyecciones. Revista De Matemática, 23(3), 187-203. https://doi.org/10.4067/S0716-09172004000300001
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Artículos