Relative mmp without $ \mathbb{Q} $-factoriality

Abstract

<p style='text-indent:20px;'>We consider the minimal model program for varieties that are not <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{Q}$\end{document}</tex-math></inline-formula>-factorial. We show that, in many cases, its steps are simpler than expected. The main applications are to log terminal singularities, removing the earlier <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{Q} $\end{document}</tex-math></inline-formula>-factoriality assumption from several theorems of Hacon-Witaszek and de Fernex-Kollár-Xu.</p>