论文标题
关于广义对的连接原理和双重复合物
On the connectedness principle and dual complexes for generalized pairs
论文作者
论文摘要
令$（x，b）$为一对，让$ f \ colon x \ rightarrow s $成为$ - （k_x + b）$ nef $ s $的收缩。一个被称为shokurov-kollár连接性的猜想预测，$ f^{ - 1}（s）\ cap \ mathrm {nklt}（x，x，b）$最多具有两个相互关联的组件，其中$ s \ in s $ in s $是任意的示意点和$ \ m nyrm $ \ nyrm { $（x，b）$。在这项工作中，我们证明了这个猜想，描述了$ \ mathrm {nklt}（x，b）$无法连接的那些情况，并且我们也将这些相同的结果扩展到了广义对的类别。最后，我们将这些结果和技术应用于对双重复合物的研究，用于概括的calabi-yau对，从而概括了Kollár-Xu和Nakamura的结果。
Let $(X,B)$ be a pair, and let $f \colon X \rightarrow S$ be a contraction with $-(K_X + B)$ nef over $S$. A conjecture, known as the Shokurov-Kollár connectedness principle, predicts that $f^{-1} (s) \cap \mathrm{Nklt}(X,B)$ has at most two connected components, where $s \in S$ is an arbitrary schematic point and $\mathrm{Nklt}(X,B)$ denotes the non-klt locus of $(X,B)$. In this work, we prove this conjecture, characterizing those cases in which $\mathrm{Nklt}(X,B)$ fails to be connected, and we extend these same results also to the category of generalized pairs. Finally, we apply these results and the techniques to the study of the dual complex for generalized log Calabi-Yau pairs, generalizing results of Kollár-Xu and Nakamura.
