On the connectedness principle and dual complexes for generalized pairs

Let be a pair, and let be a contraction with nef over S. A conjecture, known as the Shokurov-Kollár connectedness principle, predicts that has at most two connected components, where is an arbitrary schematic point and denotes the non-klt locus of. In this work, we prove this conjecture, characterizing those cases in which 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 [Invent. Math. 205 (2016), 527-557] and Nakamura [Int. Math. Res. Not. IMRN 13 (2021), 9802-9833].

Duke Scholars

Author Stefano Filipazzi Mathematics