Geometric Shafarevich boundedness conjecture for families of polarized varieties

TL;DR

This paper proves the geometric Shafarevich boundedness conjecture for the moduli stack of stable minimal models, advancing understanding of the boundedness of families of polarized varieties.

Contribution

It establishes the conjecture for the moduli stack of stable minimal models, including KSB pairs, providing new insights into the structure of these moduli spaces.

Findings

Proves the geometric Shafarevich boundedness conjecture for stable minimal models.

Includes the case of KSB pairs.

Enhances understanding of the boundedness of polarized varieties.

Abstract

We establish the geometric Shafarevich boundedness conjecture for the moduli stack of stable minimal models, including in particular the moduli stack of KSB pairs.