FAMILIES OF RIEMANN SURFACES, UNIFORMIZATION AND ARITHMETICITY

Primer Autor
Gonzalez-Diez, Gabino
Co-autores
Reyes-Carocca, Sebastian
Título
FAMILIES OF RIEMANN SURFACES, UNIFORMIZATION AND ARITHMETICITY
Editorial
AMER MATHEMATICAL SOC
Revista
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Lenguaje
en
Resumen
A consequence of the results of Bers and Griffiths on the uniformization of complex algebraic varieties is that the universal cover of a family of Riemann surfaces, with base and fibers of finite hyperbolic type, is a contractible 2 dimensional domain that can be realized as the graph of a holomorphic motion of the unit disk. In this paper we determine which holomorphic motions give rise to these uniformizing domains and characterize which among them correspond to arithmetic families (i.e. families defined over number fields). Then we apply these results to characterize the arithmeticity of complex surfaces of general type in terms of the biholomorphism class of the 2 dimensional domains that arise as universal covers of their Zariski open subsets. For the important class of Kodaira fibrations this criterion implies that arithmeticity can be read from the universal cover. All this is very much in contrast with the corresponding situation in complex dimension one, where the universal cover is always the unit disk.
Tipo de Recurso
Artículo original
Description
Both authors were partially supported by Spanish MEyC Grant MTM 2012-31973., The second author was also partially supported by Becas Chile, Universidad de La Frontera, Fondecyt Postdoctoral Project 3160002 and Project Anillo ACT1415 PIA CONICYT.
Ambos autores fueron financiados parcialmente por la Beca MEyC española MTM 2012-31973. El segundo autor también fue financiado parcialmente por Becas Chile, Universidad de La Frontera, Proyecto Postdoctoral Fondecyt 3160002 y Proyecto Anillo ACT1415 PIA CONICYT.
doi
10.1090/tran/6988
Formato Recurso
pdf
Palabras Claves
Holomorphic families of Riemann surfaces# complex surfaces and their universal covers# fields of definition# holomorphic motions
Ubicación del archivo
http://dx.doi.org/10.1090/tran/6988
Categoría OCDE
Mathematics
Materias
Familias holomorfas de superficies de Riemann# superficies complejas y sus revestimientos universales# campos de definición# movimientos holomorfos
Disciplinas de la OCDE
Matemáticas Puras
Matemáticas Aplicadas
Otras Especialidades de Matemáticas
Id de Web of Science
WOS:000418694400002
Título de la cita (Recomendado-único)
FAMILIES OF RIEMANN SURFACES, UNIFORMIZATION AND ARITHMETICITY
Identificador del recurso (Mandatado-único)
Artículo original
Versión del recurso (Recomendado-único)
version publicada
Editorial
AMER MATHEMATICAL SOC
Revista/Libro
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Categoría WOS
Matemáticas
ISSN
0002-9947
Idioma
en
Referencia del Financiador (Mandatado si es aplicable-repetible)
ANID FONDECYT 3160002#ANID Project Anillo ACT1415
MINECO MTM 2012-31973
ANID Becas Chile
UFRO
ANID FONDECYT 3160002
ANID CONICYTAnillo ACT1415 PIA CONICYT
Descripción
Both authors were partially supported by Spanish MEyC Grant MTM 2012-31973., The second author was also partially supported by Becas Chile, Universidad de La Frontera, Fondecyt Postdoctoral Project 3160002 and Project Anillo ACT1415 PIA CONICYT.
Formato
pdf
Tipo de ruta
dorada
Access Rights
acceso abierto
Derechos de acceso
acceso abierto
Página de inicio (Recomendado-único)
201
Página final (Recomendado-único)
230
Colecciones
Colección Publicaciones Científicas
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