Hyperbolicity of bases of log Calabi-Yau families

Ya Deng

Hyperbolicity of bases of log Calabi-Yau families

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arxiv 1901.04423 v2 pith:SDD47WG4 submitted 2019-01-14 math.AG math.CV

Ya Deng This is my paper · ORCID

classification math.AGmath.CV

keywords basecalabi-yaufamilyhyperbolicbasesbrodyeffectivelyfamilies

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In this paper, we prove that the quasi-projective base of any maximally variational smooth family of Calabi-Yau klt pairs is both of log general type, and pseudo Kobayashi hyperbolic. Moreover, such a base is Brody hyperbolic if the family is effectively parametrized.

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Variation of singular K\"ahler-Einstein metrics: Kodaira dimension zero
math.DG 2019-08 conditional novelty 8.0 of 10

Under a Hermitian flatness condition on the direct image of the relative log-canonical bundle, a Kähler fibration with klt log Calabi-Yau fibers is locally trivial; a K3 example shows the relative Ricci-flat metric ne...

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