A characterization of q-hyperelliptic compact planar Klein surfaces
type: Item
instance of: scholarly article
title: A characterization of q-hyperelliptic compact planar Klein surfaces
zbMATH Open document ID: 0703.30041
DOI: 10.1007/BF02941371
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1988-01-01T00:00:00Z
review text: 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 \(<\phi >\cong \Gamma_ 1/\Gamma\). Necessary and sufficient conditions on \(\Gamma_ 1\) 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.
Mathematics Subject Classification ID: 30F50
Mathematics Subject Classification ID: 14H99
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 4152810
zbMATH Keywords: Klein surface
zbMATH Keywords: non-Euclidean crystallographic group
author: Emilio Bujalance
author: José Javier Etayo
reviewed by: C. Maclachlan
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02941371
OpenAlex ID: W2004728241
description: scientific article; zbMATH DE number 4152810