Structure of the Anticanonical Minimal Model Program for Potentially klt Pairs

TL;DR

This paper provides an alternative proof for the existence of the anticanonical minimal model program for potentially klt pairs under certain conditions and establishes a structure theorem for lifting partial MMP sequences.

Contribution

It offers a new proof approach and a structure theorem for the anticanonical MMP in the context of potentially klt pairs, enhancing understanding of their birational geometry.

Findings

Proves the existence of the anticanonical minimal model program under a birational Zariski decomposition assumption.

Shows that partial anticanonical MMP sequences can be lifted to compatible maps between $ ext{Q}$-factorial terminalizations.

Establishes a structure theorem for the sequence of steps in the MMP for potentially klt pairs.

Abstract

We give an alternative proof of the existence of the anticanonical minimal model program for potentially klt pairs, assuming the anticanonical divisor admits a birational Zariski decomposition. Moreover, we establish a structure theorem showing that any partial anticanonical MMP starting from a potentially klt pair can be lifted to a compatible sequence of nonpositive maps between the $\mathbb{Q}$-factorial terminalizations of its successive steps.