Hyperbolicity of bases of log Calabi-Yau families
Ya Deng
TL;DR
This paper proves that the base of certain Calabi-Yau families is of log general type and hyperbolic, with stronger hyperbolicity if the family is effectively parametrized, advancing understanding of their geometric properties.
Contribution
It establishes that the base of maximally variational Calabi-Yau families is both of log general type and pseudo Kobayashi hyperbolic, with Brody hyperbolicity under effective parametrization.
Findings
Base is of log general type
Base is pseudo Kobayashi hyperbolic
Brody hyperbolic if family is effectively parametrized
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Geometric Analysis and Curvature Flows