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Families of canonically polarized varieties over surfaces

Stefan Kebekus·Sandor J. Kovacs
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Abstract

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.

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Stefan Kebekus, Sandor J. Kovacs. 2006-09-07. Families of canonically polarized varieties over surfaces. https://arxiv.org/abs/math/0511378

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