Hyperbolicity of bases of log Calabi-Yau families

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.

arXiv comment17 pages, v2: references added; more details and explanations on the proof of Thm. 2.2, in particular, the relations between two Higgs bundles therein are shown in a more direct way. Any comment is very welcome!

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Cited by in corpus (4)

• On the hyperbolicity of base spaces for maximally variational families of smooth projective varieties
• Big Picard theorem for moduli spaces of polarized manifolds
• Degenerated Calabi-Yau varieties with infinite components, Moduli compactifications, and limit toroidal structures
• On log minimality of weak K-moduli compactifications of Calabi-Yau varieties