Families of canonically polarized varieties over surfaces
Algebraic Geometry
2007-05-23 v4
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.
Keywords
Cite
@article{arxiv.math/0511378,
title = {Families of canonically polarized varieties over surfaces},
author = {Stefan Kebekus and Sandor J. Kovacs},
journal= {arXiv preprint arXiv:math/0511378},
year = {2007}
}
Comments
final version, to appear in Invent. Math. A rather minor issue in construction 6.10 and a typo has been fixed