论文标题
在相对最小的模型程序中，用于正面和混合特征的四倍
On the relative Minimal Model Program for fourfolds in positive and mixed characteristic
论文作者
论文摘要
我们展示了特征性$ p> 5 $的两个特殊最小模型程序的两个特殊案例的有效性：对于$ \ mathbb {q} $ - forterial四倍的收缩和曲线（“半稳定MMP”）的家庭。我们还提供了它们的混合特征类似物。作为推论，我们表明，在最小模型程序下，阳性特征三倍的可释放性是稳定的，而三维Calabi-yau品种的升降性是一种birational不变性。我们的结果部分取决于日志分辨率的存在。
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.
