Families of canonically polarized varieties over surfaces

2005/11/15 by Stefan Kebekus, Kebekus, Stefan, Sándor J. Kovács +1 · 1 citation
Mathematics · #14D20 #14D22 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0511378

openalex publication_date 2005/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Stratified Hyperbolicity of the moduli stack of stable minimal models, I

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