BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yuji Odaka (Kyoto University) DTSTART:20201126T100000Z DTEND:20201126T110000Z DTSTAMP:20260423T021405Z UID:ZAG/72 DESCRIPTION:Title: On compactifying moduli and degenerations of K-trivial varieties\nby Yuji Odaka (Kyoto University) as part of ZAG (Zoom Algebraic Geometry) seminar \n\n\nAbstract\nSome background review: the KSBA moduli of varieties of am ple canonical classes is interpreted via K-stability resp.\, KE metrics (O ’10\, resp.\, Berman-Guenancia’13). A recent trend since 2012 is to es tablish its Fano analogue\, and study their K-stability itself\, which sti ll continues to be developed by more and more contributors wonderfully. Lu ckily\, in both cases\, K-polystable / KE varieties (should) form projecti ve (compact) moduli schemes.\nHowever\, nevertheless of general K-moduli e xpectation\, such existence of projective moduli of K-polystable/cscK (pol arized) varieties is NOT true “at the boundary”\, even for classical K -trivial / Calabi-Yau cases. Indeed\, as a general theory\, no “canonica l” algebro-geometric compactification theory of moduli of polarized CY v ars seems established. E.g. An idea pursued and fairly developed is to att ach ample extra divisors on the CY vars (to pass to “K:ample”-like sit uations) and take their “log KSBA” compactifications\, but different c hoice of the extra divisors can lead to different log KSBA compactificatio ns.\nIn our talk\, based on our several recent papers (partially j.w.w. Yo shiki Oshima)\, we discuss the possibilities of still getting “canonical (geometric) compactifications” of the moduli of polarized K-trivial / CY varieties and corresponding "canonical limits"\, especially giving mor e explicit conjectures in hyperKahler / K3 case\, with certain confirmatio ns. This involves not only classical AG but also DG of collapsing CY metri cs\, symmetric space theory (Lie\, Cartan\, .. Satake..)\, non-archimedean /tropical geometry\, and some mirror symmetric phenomena. Examples and pic tures will be used for the illustration.\n LOCATION:https://researchseminars.org/talk/ZAG/72/ END:VEVENT END:VCALENDAR