Abstract
AbstractWe show the validity of two special cases of the four-dimensional minimal model program (MMP) in characteristic$p>5$: for contractions to${\mathbb {Q}}$-factorial fourfolds and in families over curves (‘semistable MMP’). We also provide their mixed characteristic analogues. As a corollary, we show that liftability of positive characteristic threefolds is stable under the MMP and that liftability of three-dimensional Calabi–Yau varieties is a birational invariant. Our results are partially contingent upon the existence of log resolutions.
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