Bujalance, E. and Etayo Gordejuela, J. Javier and Gamboa Mutuberria, José Manuel (1985) Hyperelliptic Klein surfaces. Quarterly Journal of Mathematics , 36 (2). pp. 141-157. ISSN 0033-5606
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.
|Uncontrolled Keywords:||Classification theory of Riemann surfaces; Coverings, fundamental group; Fuchsian groups and their generalizations|
|Subjects:||Sciences > Mathematics > Algebraic geometry|
|Deposited On:||25 Jun 2012 10:52|
|Last Modified:||25 Jun 2012 10:52|
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