Bujalance, E.Etayo Gordejuela, José Javier2023-06-202023-06-201988Bujalance, E., & Etayo Gordejuela, J. J. «A Characterization of Q-Hyperelliptic Compact Planar Klein Surfaces». Abhandlungen Aus Dem Mathematischen Seminar Der Universität Hamburg, vol. 58, n.o 1, diciembre de 1988, pp. 95-102. DOI.org (Crossref), https://doi.org/10.1007/BF02941371.0025-585810.1007/BF02941371https://hdl.handle.net/20.500.14352/57397A 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.journal articlehttps//doi.org/10.1007/BF02941371http://www.springerlink.com/content/1ru7742hg4x102r8/metadata only access512.54Compact Riemann surfaces and uniformizationFuchsian groups and their generalizationsGeometria algebraicaGrupos (Matemáticas)1201.01 Geometría Algebraica