On weak Zariski decompositions and termination of flips

TL;DR

This paper establishes that the termination of flips in lower dimensions and the existence of weak Zariski decompositions are interconnected, leading to the existence of minimal models for generalized pairs.

Contribution

It proves that lower-dimensional flip termination implies flip termination for generalized pairs with weak Zariski decompositions, and links these decompositions to minimal model existence.

Findings

Termination of flips in lower dimensions implies termination for generalized pairs.

Existence of weak Zariski decompositions leads to minimal models.

Connections between Zariski decompositions and the minimal model program.

Abstract

We prove that termination of lower dimensional flips for generalized klt pairs implies termination of flips for log canonical generalized pairs with a weak Zariski decomposition. Moreover, we prove that the existence of weak Zariski decompositions for pseudo-effective generalized klt pairs implies the existence of minimal models for such pairs.