Hyperbolicity of bases of log Calabi-Yau families
arXiv:1901.04423
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.
17 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!