On the relative minimal model program for fourfolds in positive and mixed characteristic
On the relative minimal model program for fourfolds in positive and mixed characteristic
复制标题
DOI：
10.1017/fmp.2023.6
复制
发表时间：
2020-09
期刊：
影响因子：
--
通讯作者：
Christopher D. Hacon;J. Witaszek
中科院分区：
文献类型：
--
作者：
Christopher D. Hacon;J. Witaszek
摘要我们证明了四维最小模型程序的两个特例的有效性：对于$p>；5$-阶乘四重收缩和曲线上的族(半稳定的)。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升性在最小二乘法下是稳定的，并且三维Calabi-Yau变种的可升性是一个二次不变量。我们的结果在一定程度上取决于对数解的存在。
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.