|Date: Tuesday, October 23, 2012
Title: On complex hyperbolicity of moduli spaces of canonically polarized algebraic manifolds
Abstract: The purpose of the talk is to introduce the notions and explain a result on hyperbolicity of moduli spaces of canonically polarized algebraic manifolds, or equivalently moduli spaces of Kaehler-Einstein manifolds of negative scalar curvature. It is a classical fact from the work of Ahlfors, Royden and Wolpert that the Weil-Petersson metric on a moduli space of hyperbolic Riemann surface has holomorphic sectional curvature bounded from above by a negative constant and hence is Kobayashi hyperbolic. A natural question is whether similar properties hold in a higher dimensional analogue. I would explain a joint work with Wing-Keung To on the construction of a negatively curved Finsler metric on any moduli space of Kaehler-Einstein manifolds with negative scalar curvature, from which Kobayashi hyperbolicity follows naturally.
Speaker: Sai-Kee Yeung
Institution: Purdue University