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

TL;DR

This paper explores the hyperbolic geometry of the base space of certain algebraic families of stable minimal models, using advanced Hodge theory techniques.

Contribution

It constructs Higgs sheaves for admissible families of lc stable minimal models, linking hyperbolicity with Hodge theory and degenerations.

Findings

Establishes hyperbolicity properties of the moduli stack

Constructs Higgs sheaves from degenerations of Hodge structures

Connects geometric stability with Hodge-theoretic methods

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.