Repositorio
Institucional

Gonzalez-Diez, Gabino

Reyes-Carocca, Sebastian

FAMILIES OF RIEMANN SURFACES, UNIFORMIZATION AND ARITHMETICITY

AMER MATHEMATICAL SOC

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

en

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.

Artículo original

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.

10.1090/tran/6988

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Holomorphic families of Riemann surfaces# complex surfaces and their universal covers# fields of definition# holomorphic motions

http://dx.doi.org/10.1090/tran/6988

Mathematics

Familias holomorfas de superficies de Riemann# superficies complejas y sus revestimientos universales# campos de definición# movimientos holomorfos

Matemáticas Puras

Matemáticas Aplicadas

Otras Especialidades de Matemáticas

WOS:000418694400002

FAMILIES OF RIEMANN SURFACES, UNIFORMIZATION AND ARITHMETICITY

Artículo original

version publicada

AMER MATHEMATICAL SOC

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Matemáticas

0002-9947

en

ANID FONDECYT 3160002#ANID Project Anillo ACT1415

MINECO MTM 2012-31973

ANID Becas Chile

UFRO

ANID FONDECYT 3160002

ANID CONICYTAnillo ACT1415 PIA CONICYT

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.

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