Quasi-Projective Moduli for Polarized klt Good Minimal Models

Abstract

We prove the weak positivity of direct images for locally stable families of klt good minimal models over reduced quasi-projective bases using Gabber's Extension Theorem. As an application, we apply Viehweg's ampleness criterion to show that the normalization of the moduli space of polarized klt good minimal models of arbitrary Kodaira dimension, constructed in [Jia23], is quasi-projective.