Families of canonically polarized varieties over surfaces

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Shafarevich's hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial unless the logarithmic Kodaira dimension of the base is positive. More generally it has been conjectured by Viehweg that the base of a smooth family of canonically polarized varieties is of log general type if the family is of maximal variation. In this paper, we relate the variation of a family to the logarithmic Kodaira dimension of the base and give an affirmative answer to Viehweg's conjecture for families parametrized by surfaces.
final version, to appear in Invent. Math. A rather minor issue in construction 6.10 and a typo has been fixed

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Algebraic Geometry, 14D20, 14D22

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http://salesiana.dossiersoluciones.com/handle/123456789/104931

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511378
 http://arxiv.org/abs/math/0511378

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arXiv