Uniformizations of stable (γ,n)-gonal Riemann surfaces

Primer Autor
Hidalgo, Ruben A.
Título
Uniformizations of stable (γ,n)-gonal Riemann surfaces
Editorial
SPRINGER BASEL AG
Revista
ANALYSIS AND MATHEMATICAL PHYSICS
Lenguaje
en
Resumen
A (., n)-gonal pair is a pair (S, f), where S is a closed Riemann surface and f : S. R is a degree n holomorphic map onto a closed Riemann surface R of genus.. If the signature of (S, f) is of hyperbolic type, then it admits a uniformizing pair (G, G), where G is a Fuchsian group acting on the unit disc D containing G as an index n subgroup, such that f is induced by the inclusion G = G. The uniformizing pair is uniquely determined by (S, f), up to conjugation by holomorphic automorphisms of D, and it permits to provide a natural complex orbifold structure on the Hurwitz space parametrizing (twisted) isomorphic classes of pairs topologically equivalent to (S, f). In order to produce certain compactifications of these Hurwitz spaces, one needs to consider the so called stable (., n)-gonal pairs, which are natural geometrical deformations of (., n)-gonal pairs. Due to the above, it seems interesting to search for uniformizations of stable (., n)-gonal pairs, in terms of certain class of Kleinian groups. In this paper we review such uniformizations by using noded Fuchsian groups, obtained from the noded Beltrami differentials of Fuchsian groups that were previously studied by Alexander Vasil'ev and the author, and which provide uniformizations of stable Riemann orbifolds. These uniformizations permit to obtain a compactification of the Hurwitz spaces together a complex orbifold structure, these being quotients of the augmented Teichmuller space of G by a suitable finite index subgroup of its modular group.
Tipo de Recurso
Artículo original
Description
Supported by Project Fondecyt 1150003 and Project Anillo ACT1415 PIA CONICYT.
Con apoyo del Proyecto Fondecyt 1150003 y Proyecto Anillo ACT1415 PIA CONICYT.
doi
10.1007/s13324-018-0253-5
Formato Recurso
pdf
Palabras Claves
Riemann surfaces# Fuchsian groups# Teichmuller space# Quasiconformal maps
Ubicación del archivo
http://dx.doi.org/10.1007/s13324-018-0253-5
Categoría OCDE
Mathematics, Applied# Mathematics
Materias
superficies de Riemann# grupos fucsianos# espacio de Teichmüller# Mapas cuasiconformes
Disciplinas de la OCDE
Matemáticas Puras
Matemáticas Aplicadas
Otras Especialidades de Matemáticas
Id de Web of Science
WOS:000451394300011
Título de la cita (Recomendado-único)
Uniformizations of stable (γ,n)-gonal Riemann surfaces
Identificador del recurso (Mandatado-único)
Artículo original
Versión del recurso (Recomendado-único)
version publicada
Editorial
SPRINGER BASEL AG
Revista/Libro
ANALYSIS AND MATHEMATICAL PHYSICS
Categoría WOS
Matemáticas Aplicadas# Matemáticas
ISSN
1664-2368
Idioma
en
Referencia del Financiador (Mandatado si es aplicable-repetible)
ANID FONDECYT 1150003#ANID ACT1415
ANID FONDECYT 1150003
ANID ACT1415 PIA CONICYT
Descripción
Supported by Project Fondecyt 1150003 and Project Anillo ACT1415 PIA CONICYT.
Formato
pdf
Tipo de ruta
hibrida#verde
Access Rights
acceso abierto
Derechos de acceso
acceso abierto
Página de inicio (Recomendado-único)
823
Página final (Recomendado-único)
832
Colecciones
Colección Publicaciones Científicas
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