正特性和混合特性的四倍相对最小模型程序

IF 2.8 1区数学 Q1 MATHEMATICS

Forum of Mathematics Pi Pub Date : 2020-09-06 DOI:10.1017/fmp.2023.6

C. Hacon, J. Witaszek

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引用次数: 9

摘要

摘要我们证明了特征$p>5$中四维最小模型程序（MMP）的两种特殊情况的有效性：收缩到${\mathbb{Q}}$阶乘四倍和在曲线上的族中（“化学MMP”）。我们还提供了它们的混合特征类似物。作为推论，我们证明了正特征三重的可举性在MMP下是稳定的，并且三维Calabi–Yau品种的可举度是双条件不变量。我们的结果部分取决于日志分辨率的存在。

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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 $p>5$ : 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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来源期刊

Forum of Mathematics Pi Mathematics-Statistics and Probability

CiteScore

3.50

自引率

0.00%

发文量

审稿时长

19 weeks

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