Families of canonically polarized varieties over surfaces
成果类型：
Article
署名作者：
Kebekus, Stefan; Kovacs, Sandor J.
署名单位：
University of Cologne; University of Washington; University of Washington Seattle
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-008-0128-8
发表日期：
2008
页码：
657-682
关键词：
摘要：
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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