Bujalance, E. and Etayo Gordejuela, J. Javier and Gamboa, J. M.
(1985)
*Hyperelliptic Klein surfaces.*
Quarterly Journal of Mathematics , 36
(2).
pp. 141-157.
ISSN 0033-5606

Official URL: http://qjmath.oxfordjournals.org/content/36/2/141.extract

## Abstract

A compact Klein surface can be represented in the form D/Γ where D denotes the hyperbolic plane and Γ a non-Euclidean crystallographic (N.E.C.) group of isometries. If Γ + denotes the subgroup of orientation-preserving isometries, then D/Γ + is conformally equivalent to a compact Riemann surface; and if it is hyperelliptic, then D/Γ is called a hyperelliptic Klein surface (H.K.S.). This paper extends the results of the reviewer [same journal Ser. (2) 22 (1971) 117--123; MR0283194 (44 #427)] to characterise H.K.S. and their smooth normal hyperelliptic coverings via N.E.C. groups and their signatures. In addition, the number of hyperelliptic coverings of a given H.K.S. is computed and all results translated into the language of real algebraic curves.

Item Type: | Article |
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Uncontrolled Keywords: | Classification theory of Riemann surfaces; Coverings, fundamental group; Fuchsian groups and their generalizations |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 15747 |

Deposited On: | 25 Jun 2012 08:52 |

Last Modified: | 01 Mar 2016 18:09 |

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