Finsler metrics and Kobayashi hyperbolicity of the moduli spaces of canonically polarized manifolds

  title={Finsler metrics and Kobayashi hyperbolicity of the moduli spaces of canonically polarized manifolds},
  author={Wing-Keung To and Sai-Kee Yeung},
  journal={Annals of Mathematics},
We show that the base complex manifold of an eectively parametrized holomorphic family of compact canonically polarized complex manifolds admits a smooth invariant Finsler metric whose holomorphic sectional curvature is bounded above by a negative constant. As a consequence, we show that such a base manifold is Kobayashi hyperbolic. 

Augmented Weil–Petersson metrics on moduli spaces of polarized Ricci-flat Kähler manifolds and orbifolds

. We show that the base complex manifold of an effectively parametrized family of compact polarized Ricci-flat K¨ahler orbifolds, and in particular manifolds, admits a smooth augmented Weil-Petersson

Holomorphic Sectional Curvature of Complex Finsler Manifolds

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    Journal of geometric analysis
  • 2019
An inequality in terms of holomorphic sectional curvature of complex Finsler metrics is obtained and a Schwarz Lemma from a complete Riemannian manifold to a complex F Insler manifold is proved.

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

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In recent years, there are quite a lot of interests and results related to hyperbolicity properties of the base spaces of various families of projective algebraic varieties. Not much is known for

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Brody hyperbolicity of base spaces of certain families of varieties

We prove that quasi-projective base spaces of smooth families of minimal varieties of general type with maximal variation do not admit Zariski dense entire curves. We deduce the fact that moduli



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The Curvature of the Petersson-Weil Metric on the Moduli Space of Kähler-Einstein Manifolds

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Extremal bounded holomorphic functions and an embedding theorem for arithmetic varieties of rank ≥ 2

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Quasi-projective moduli for polarized manifolds

  • E. Viehweg
  • Mathematics
    Ergebnisse der Mathematik und ihrer Grenzgebiete
  • 1995
This text discusses two subjects of quite different natures: construction methods for quotients of quasi-projective schemes either by group actions or by equivalence relations; and properties of

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Given a family $f:\mathcal{X} \to S$ of canonically polarized manifolds, the unique Kähler–Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle

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We prove that the defect vanishes for a holomorphic map f from the affine complex line to an abelian variety A and for an ample divisor D in A. The proof uses the translational invariance of the

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