Boundedness of klt good minimal models

TL;DR

This paper proves that klt good minimal models with certain polarized divisors form a bounded family when fixing numerical invariants, and constructs moduli spaces for these models.

Contribution

It establishes boundedness of klt good minimal models with Weil divisors and constructs separated moduli spaces for them.

Findings

Boundedness of klt good minimal models with fixed invariants.

Construction of separated coarse moduli spaces for these models.

Application to moduli theory of algebraic varieties.

Abstract

For good minimal models with klt singularities, polarized by Weil divisors that are relatively nef and big over the bases of the Iitaka fibration, we show that, after fixing appropriate numerical invariants, they form a bounded family. As an application, we construct separated coarse moduli spaces for klt good minimal models polarized by line bundles.