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

@article{To2015FinslerMA, 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}, year={2015}, volume={181}, pages={547-586} }

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.

## 43 Citations

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