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Complex Analysis and Geometry Seminar

"Hyperbolicity of some moduli spaces of polarized manifolds"

Date & time: Friday, 31 March 2017 at 2:00PM -


Sai-Kee Yeung, Purdue University

"Hyperbolicity of some moduli spaces of polarized manifolds"

Time: 2:00 PM
Location: Hill 705
Abstract: In this talk, we would explain some joint work with Wing-Keung To on hyperbolicity of moduli spaces of polarized algebraic manifolds, including families or moduli spaces of Kaehler-Einstein manifolds of negative scalar curvature or trivial scalar curvature, and some log-general type manifolds for quasi-projective versions. Classically, results on moduli space of Riemann surfaces of genus at least two have been obtained by Ahlfors, Royden and Wolpert with Weil-Petersson metric. Study of moduli of higher dimensional manifolds in terms of Weil-Petersson metrics began with a work of Siu thirty years ago. Eventually, we construct a negatively curved Finsler metric on such moduli from which results in hyperbolicity follow naturally. We also apply the related techniques to study questions related to a conjecture of Viehweg.

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