BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stefano Filipazzi (UCLA) DTSTART:20210223T153000Z DTEND:20210223T163000Z DTSTAMP:20260412T202950Z UID:fano2021/4 DESCRIPTION:Title: On the connectedness principle and dual complexes for generalized pairs\nby Stefano Filipazzi (UCLA) as part of Fano Varieties and Birational G eometry\n\n\nAbstract\nLet (X\,B) be a pair (a variety with an effective Q -divisor)\, and let f: X -> S be a contraction with -(K_X+B) nef over S. A conjecture\, known as the Shokurov-Koll\\'ar connectedness principle\, pr edicts that f^{-1}(s) intersect Nklt(X\,B) has at most two connected compo nents\, where s is an arbitrary point in S and Nklt(X\,B) denotes the non- klt locus of (X\,B). The conjecture is known in some cases\, namely when - (K_X+B) is big over S\, and when it is Q-trivial over S. In this talk\, we discuss a proof of the full conjecture and extend it to the case of gener alized pairs. Then we apply it to the study of the dual complex of general ized log Calabi-Yau pairs. This is joint work with Roberto Svaldi.\n LOCATION:https://researchseminars.org/talk/fano2021/4/ END:VEVENT END:VCALENDAR