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Título:
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A characterization of q-hyperelliptic compact planar Klein surfaces
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Autores:
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Bujalance, E. ;
Etayo Gordejuela, J. Javier
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Tipo de documento:
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texto impreso
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Editorial:
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Springer, 1988
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Geometria algebraica
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Materia = Ciencias: Matemáticas: Grupos (Matemáticas)
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Tipo = Artículo
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Resumen:
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A compact Klein surface X is called q-hyperelliptic if there is an involution $\phi$ of X such that the quotient surface $X/$ 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 $\cong \Gamma\sb 1/\Gamma$. 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.
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