ϒ-hyperelliptic Riemann surfaces

Rubén A. Hidalgo

Resumen


We give some characterizations of ϒ -hyperelliptic Riemann surfaces of genus ɡ ≥ 2, that is, pairs (S, j) where S is a closed Riemann surface of genus ɡ and j : SS is a conformal involution with exactly 2ɡ + 2 - 4ϒ  fixed points. These characterizations are given by Schottky groups, special hyperbolic polygons and algebraic curves.

These can be seen as generalizations of the works [5] and [11].


Palabras clave


Puchsian groups ; Schottky groups ; Riemann surfaces

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Referencias


Ahlfors, L. V. and Sario, L., "Riemann surfaces", Princeton Univ. Press. Princeton, New Jersey, (1960).

Bers, L., Uniformization by Beltrami equations, Comm. Pure Appl. Math. 14, pp. 215-228, (1961).

Chuckrow, V., On Schottky groups with applications to Kleinian groups, Ann. of Math. 88, pp. 47-61, (1968).

Farkas, H. and Kra, I., "Riemann surfaces", Springer-Verlag.

Gallo, D., Hyperelliptic Riemann surfaces, thesis Ph.D. S.U.N.Y. at Stony Brook, (1979).

Haas, A. and Susskind,. P., The geometry of the hyperelliptic involution in genus two,

Hejhal, D. A., On Schottky and Teichmüller spaces, Adv. in Math. 15, pp. 133-156, (1975).

Hidalgo, R., On ϒ -hyperelliptic Schottky groups, Boletín de la Sociedad de Matemática de Chile, 8, pp. 27-36, (1989).

Hidalgo, R., On Schottky Groups with Automorphisms, thesis Ph.D. in Math. S.U.N.Y. at Stony Brook, New York, (1991).

Hiro-0 Yamamoto, An example of a nonclassical Schottky group, Duke Math. J. 63, pp. 193-197, (1991).

Keen, L., On hyperelliptic Schottky groups, Annales Academiae Scientianun Fennicae. Series A.I. Mathematica, volumen 5, pp. 165-174, (1980).

Keen, L., Canonical polygons for finitely generated Fuchsian groups, Acta Mathematica 115, (1966).

Maskit, B., Kleinian groups, Springer-Verlag.

Maskit, B., Decomposition of certain Kleinian groups, Acta Mathematica, vol 130, (1973).

Marden, A., Schottky groups and circles, in Contribution to Analysis: A collection of Papers Dedicated to Lipman Bers, ed. Lars V. Ahlfors, et. al., Academic Press, New York, pp. 273-278, (1964).

Whittaker, E., On the connection of algebraic functions with automorphic functions, Phil. Trans., vol 192, pp. 1-32, (1899)




DOI: http://dx.doi.org/10.22199/S07160917.1998.0001.00007

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