Moduli of canonically polarized manifolds, higher order Kodaira-Spencer maps, and an analogy to Calabi-Yau manifolds

Abstract

A Finsler metric, whose holomorphic curvature is bounded from above by a negative constant, is constructed on the moduli stack of canonically polarized manifolds including singularities. Demailly's version of Ahlfors' lemma yields hyperbolicity of the moduli stack.

Abstract added, minor changes. To appear in "Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds, and Picard-Fuchs Equations"

Cited by in corpus (3)

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• On the hyperbolicity of base spaces for maximally variational families of smooth projective varieties
• Big Picard theorem for moduli spaces of polarized manifolds