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 (2)

• Desingularization of quasi-excellent schemes in characteristic zero
• Resolution and alteration with ample exceptional divisor