### Impacto

Bujalance, E. and Etayo Gordejuela, J. Javier
(1988)
*A characterization of q-hyperelliptic compact planar Klein surfaces.*
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 58
(1).
pp. 95-104.
ISSN 0025-5858

Official URL: http://www.springerlink.com/content/1ru7742hg4x102r8/

## Abstract

A compact Klein surface X is called q-hyperelliptic if there is an involution $\phi$ of X such that the quotient surface $X/<\phi >$ has algebraic genus q. If X is represented as D/$\Gamma$ where D is the unit disc and $\Gamma$ a non-Euclidean crystallographic group, then $<\phi >\cong \Gamma\sb 1/\Gamma$. Necessary and sufficient conditions on $\Gamma\sb 1$ are determined so that X is both planar (i.e. a two-sphere with holes) and q-hyperelliptic. One of the consequences of this is that the subspace of the Teichmüller space of those compact planar surfaces of fixed algebraic genus p which are q-hyperelliptic is a submanifold of dimension 2p-q-1 in the cases where $p>4q+1$. The methods involved are standard using the structure of NEC groups.

Item Type: | Article |
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Uncontrolled Keywords: | Compact Riemann surfaces and uniformization; Fuchsian groups and their generalizations |

Subjects: | Sciences > Mathematics > Algebraic geometry Sciences > Mathematics > Group Theory |

ID Code: | 15777 |

Deposited On: | 27 Jun 2012 08:57 |

Last Modified: | 27 Jun 2012 08:57 |

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