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 need not be semipositive.
Hyperbolicity of bases of log Calabi-Yau families
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abstract
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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math.DG 1years
2019 1verdicts
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Variation of singular K\"ahler-Einstein metrics: Kodaira dimension zero
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 need not be semipositive.