Hyperbolicity of the base of an admissible family of log canonical stable minimal models

2023/02/20 by Shentu, Junchao, Zhao, Chen
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.09828

Abstract

We investigate the stratified hyperbolicity properties of Birkar's moduli stack of log canonical (lc) stable minimal models. The main technical result is a construction of Viehweg-Zuo's system of Higgs sheaves associated with an admissible family of lc stable minimal models, using the theory of degenerations of Hodge structure and non-abelian Hodge theory.

Related

• Stratified Hyperbolicity of the moduli stack of stable minimal models, I
• Stratified Hyperbolicity of the moduli stack of stable minimal models, II: Big Picard Theorem and the stratified Brody hyperbolicity
• Stable Reduction via the Log Canonical Model
• Hyperbolicity for log smooth families with maximal variation
• Log canonical singularities and complete moduli of stable pairs