Pseudo Kobayashi hyperbolicity of base spaces of families of minimal projective manifolds with maximal variation

2018/09/16 by Deng, Ya
#14C30 #14H15 #32J25 #32Q45 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.05891

Abstract

In this paper we prove that every quasi-projective base space V of smooth family of minimal projective manifolds with maximal variation is pseudo Kobayashi hyperbolic, i.e. V is Kobayashi hyperbolic modulo a proper subvariety Z\subsetneq V. In particular, V is algebraically degenerate, that is, every nonconstant entire curve f:ℂ→ V has image f(ℂ) which lies in that proper subvariety Z\subsetneq V. As a direct consequence, we prove the Brody hyperbolicity of moduli spaces of minimal projective manifolds, which answers a question by Viehweg-Zuo in 2003.

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