Special MMP for log canonical generalised pairs

TL;DR

This paper proves the existence of minimal models for certain log canonical generalized pairs under specific assumptions, advancing the minimal model program in algebraic geometry.

Contribution

It establishes the existence of minimal models for Q-factorial NQC log canonical generalized pairs assuming minimal models for smooth varieties.

Findings

Existence of minimal models for Q-factorial NQC log canonical generalized pairs.

Termination of MMP with scaling under certain conditions.

New existence results for minimal models and Mori fibre spaces.

Abstract

We show that minimal models of $\mathbb{Q}$-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a $\mathbb{Q}$-factorial NQC log canonical generalised pair $ (X,B+M) $ we can run an MMP with scaling of an ample divisor which terminates, assuming that it admits an NQC weak Zariski decomposition or that $K_X+B+M$ is not pseudoeffective. As a consequence, we establish several existence results for minimal models and Mori fibre spaces.