Relative MMP without Q-factoriality

Abstract

We consider the minimal model program for varieties that are not Q-factorial. We show that, in many cases, its steps are simpler than expected. In particular, all flips are 1-complemented. The main applications are to log terminal singularities, removing the earlier Q-factoriality assumption from several theorems of Hacon--Witaszek and de~Fernex--Kollár--Xu. Version 2: many small changes.

References in corpus (5)

• Desingularization of quasi-excellent schemes in characteristic zero
• Finiteness of algebraic fundamental groups
• Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic
• Vanishing theorems for threefolds in characteristic $p>5$
• Resolution and alteration with ample exceptional divisor

Cited by in corpus (4)

• Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic
• Minimal model program for semi-stable threefolds in mixed characteristic
• Vanishing theorems for threefolds in characteristic $p>5$
• Moishezon Spaces and Projectivity Criteria