CUBO A Mathematical Journal Vol.12, N° 01, (175-179). March 2010

 

A Short Note On M-Symmetric Hyperelliptic Riemann Surfaces *

 

Rubén A. Hidalgo

Departamento de Matemáticas, Universidad Técnica Federico Santa María, Valparaíso, Chile email : ruben.hidalgo@usm.cl

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ABSTRACT

We provide an argument, based on Schottky groups, of a result due to B. Maskit which states a necessary and sufficient condition for the double oriented cover of a planar compact Klein surface of algebraic genus at least two to be a hyperelliptic Riemann surface.

Key words and phrases: Schottky groups, Hyperelliptic Riemann surfaces.

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RESUMEN

Damos un argumento, basado en grupos de Schottky, de un resultado debido a B. Maskit el cual establece una condición necesária y suficiente para el cubrimiento duplo orientado de una superficie de Klein compacta planar de genero algebrico al menos dos ser una superficie de Riemann hipereliptica.

Math. Subj. Class.: 30F10, 30F40.

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Notas

*Partially supported by projects Fondecyt 1070271 and UTFSM 12.09.02

References

[1] Ahlfors, L. and Sario, L., Riemann Surfaces, Princeton University Press, Princeton NJ, 1960.         [ Links ]

[2] Farkas, H. and Kra, I., Riemann Surfaces, Second edition. Graduate Texts in Mathematics, 71, Springer-Verlag, New York, 1992.         [ Links ]

[3] Keen, L., On Hyperelliptic Schottky groups, Ann. Acad. Sci. Fenn. Series A.I. Mathematica, 5, 1980.         [ Links ]

[4] Maskit, B., Remarks on m-symmetric Riemann surfaces, Contemporary Math., 211 (1997), 433-445.         [ Links ]

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Received: September 2008.

Revised: January 2009.