# 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}
}
• Published 1 March 2015
• Mathematics
• 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.
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