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arXiv · 2009.02631

On the relative Minimal Model Program for fourfolds in positive and mixed characteristic

Christopher Hacon·Jakub Witaszek
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Abstract

We show the validity of two special cases of the four-dimensional Minimal Model Program in characteristic $p>5$: for contractions to $\mathbb{Q}$-factorial fourfolds and in families over curves ("semi-stable mmp"). We also provide their mixed characteristic analogues. As a corollary, we show that liftability of positive characteristic threefolds is stable under the minimal model program, 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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Christopher Hacon, Jakub Witaszek. 2020-09-06. On the relative Minimal Model Program for fourfolds in positive and mixed characteristic. https://arxiv.org/abs/2009.02631

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