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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.23 n.3 Antofagasta dic. 2004

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

 

Proyecciones
Vol. 23, No 3, pp. 187-203, December 2004.
Universidad Católica del Norte
Antofagasta - Chile

ABELIAN AUTOMORPHISMS GROUPS OF SCHOTTKY TYPE

 

RUBÉN HIDALGO *

Universidad Técnica Federico Santa María, Chile

Correspondencia a :


ABSTRACT

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 su.cient condition for H to be of Schottky type. We also give partial answers for the excluded cases.

AMS Classification : 30F10, 30F40, 30F50


References

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[3] R.A. Hidalgo and A.F. Costa. Anticonformal automorphisms and Schottky coverings. Ann. Acad. Scie. Fenn. 26, pp. 489-508, 2001.        [ Links ]

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[5] R.A. Hidalgo. On Schottky groups with automorphisms. Ann. Acad. Scie. Fenn. Ser. AI Mathematica 19, pp. 259-289, 1994.        [ Links ]

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[8] R.A. Hidalgo. A4, A5, S4 and S5 of Schottky type. Revista Matematica Complutense 15, 2002.        [ Links ]

[9] R.A. Hidalgo. Real surfaces, Riemann matrices and algebraic curves. Contemporary Mathematics 311, pp. 277-299, 2001.        [ Links ]

[10] R.A. Hidalgo. Automorphisms groups of Schottky type. preprint.         [ Links ]

[11] R.A. Hidalgo. The mixed elliptically fixed point property for Kleinian groups. Ann. Acad. Scie. Fenn. Ser. AI Mathematica 19, pp. 247-258, 1994.

[12] P. Koebe. ¨Uber die Uniformisierung der Algebraischen Kurven II, Math. Ann. 69, pp. 1-81, 1910.        [ Links ]

[13] B. Maskit. Canonical domains on Riemann surfaces. Proc. of the Amer. Math. Soc. 106, pp. 713-721, 1989.        [ Links ]

[14] Maskit, B. On the classification of Kleinian Groups II-Signatures. Acta Mathematica 138, pp. 17-42, 1977.        [ Links ]

 

*Partially supported by projects Fondecyt 1030252, 1030373 and UTFSM 12.03.21.

Received : April 2004. Accepted : October 2004

Ruben A. Hidalgo
Departamento de Matemática

Universidad Técnica Federico Santa María
Casilla 110 - V
Valparaíso
Chile
e-mail : ruben.hidalgo@mat.utfsm.cl

 

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