On the relative minimal model program for fourfolds in positive and mixed characteristic
We 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 c...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Pi |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508623000069/type/journal_article |
| Summary: | We 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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| ISSN: | 2050-5086 |