@article{9e40cdd5ac7e4ffc969c42e61ebbe061,
title = "On the relative minimal model program for fourfolds in positive and mixed characteristic",
abstract = "We show the validity of two special cases of the four-dimensional minimal model program (MMP) in characteristic 5 ]]>: for contractions to-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.",
author = "Christopher Hacon and Jakub Witaszek",
note = "Funding Information: The first author was partially supported by NSF research grants no: DMS-1300750, DMS-1952522, DMS-1801851 and by a grant from the Simons Foundation; Award Number: 256202. He would also like to thank the Mathematics Department and the Research Institute for Mathematical Sciences, located Kyoto University and the Mathematical Sciences Research Institute in Berkeley were some of this research was conducted. The second author was supported by the National Science Foundation under Grant No. DMS-1638352 at the Institute for Advanced Study in Princeton and by the National Science Foundation under Grant No. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2019 semester. He is currently supported by the NSF research grant no: DMS-2101897. Publisher Copyright: {\textcopyright} The Author(s), 2023. Published by Cambridge University Press.",
year = "2023",
month = mar,
day = "24",
doi = "10.1017/fmp.2023.6",
language = "English (US)",
volume = "11",
journal = "Forum of Mathematics, Pi",
issn = "2050-5086",
publisher = "Cambridge University Press",
}