BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Masafumi Hattori (Kyoto University) DTSTART:20220324T100000Z DTEND:20220324T110000Z DTSTAMP:20260423T021356Z UID:ZAG/196 DESCRIPTION:Title: On K-stability of Calabi-Yau fibrations\nby Masafumi Hattori (Kyoto Univ ersity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn K-stability\, the characterization of K-stable varieties is well-studied when K_X is ample or X is a Calabi-Yau or Fano variety. However\, K-stabil ity of Fano fibrations or Calabi-Yau fibrations (i.e.\, K_X is relatively trivial) is not known much in algebraic geometry. On the other hand\, cscK problems on fibrations are studied by Fine\, Jian-Shi-Song and Dervan-Sek tnan in Kahler geometry. We introduce adiabatic K-stability (If f:(X\,H)\\ to (B\,L) is a fibration of polarized varieties\, this means that K-stabil ity of (X\,aH+L) for sufficiently small a) and show that adiabatic K-semis tability of Calabi-Yau fibration implies log-twisted K-semistability of th e base variety by applying the canonical bundle formula. If the base is a curve\, we also obtain a partial converse. In this talk\, I would like to explain our main results and their applications to rational elliptic surfa ces and the conjecture of Miranda on Chow-stability of rational Weierstras s fibrations.\n LOCATION:https://researchseminars.org/talk/ZAG/196/ END:VEVENT END:VCALENDAR