论文标题
$ 3 $ folds的连接原理$ p> 5 $
Connectedness principle for $3$-folds in characteristic $p>5$
论文作者
论文摘要
一个被称为shokurov-kollár连接性原理的猜想预测了以下内容。令$（x，b）$为一对，然后让$ f \ colon x \ rightarrow s $成为$ - （k_x + b）$ nef $ s $的收缩；然后，对于任何点$ s \在s $中，相交$ f^{ - 1}（s）\ cap \ mathrm {nklt}（x，x，b）$最多具有两个连接的组件，其中$ \ mathrm {nklt}（nklt}（x，x，x，x，b）$表示non-klt locus of $（x，x，x，x，b）$（x，x，b）。该猜想已在特征零中进行了广泛的研究，并且最近在这种情况下解决了。在这项工作中，我们考虑了在积极特征代数几何形状的设置中的这种猜想。我们证明了这种猜想的特征性$ p> 5 $中的三倍，并且在相同的假设下，我们表征了$ \ mathrm {nklt}（x，b）$未连接的情况。
A conjecture, known as the Shokurov-Kollár connectedness principle, predicts the following. Let $(X,B)$ be a pair, and let $f \colon X \rightarrow S$ be a contraction with $-(K_X + B)$ nef over $S$; then, for any point $s \in S$, the intersection $f^{-1} (s) \cap \mathrm{Nklt}(X,B)$ has at most two connected components, where $\mathrm{Nklt}(X,B)$ denotes the non-klt locus of $(X,B)$. This conjecture has been extensively studied in characteristic zero, and it has been recently settled in that context. In this work, we consider this conjecture in the setup of positive characteristic algebraic geometry. We prove this conjecture holds for threefolds in characteristic $p> 5$, and, under the same assumptions, we characterize the cases in which $\mathrm{Nklt}(X,B)$ fails to be connected.
