Author:
Hacon Christopher,Witaszek Jakub
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.
Publisher
Cambridge University Press (CUP)
Subject
Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Analysis
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