Universidad Complutense de Madrid
E-Prints Complutense

Hyperelliptic Klein surfaces

Impacto

Downloads

Downloads per month over past year

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


URLURL Type
http://www.oup.com/Publisher


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
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

Origin of downloads

Repository Staff Only: item control page