BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hokuto Uehara (Tokyo Metropolitan University) DTSTART:20201224T100000Z DTEND:20201224T110000Z DTSTAMP:20260423T035821Z UID:ZAG/80 DESCRIPTION:Title: Exc eptional collections on the Hilzebruch surface of degree 2\nby Hokuto Uehara (Tokyo Metropolitan University) as part of ZAG (Zoom Algebraic Geom etry) seminar\n\n\nAbstract\nThe purpose of my talk is to clarify the stru cture of exceptional collections of the derived category of coherent sheav es on the Hirzebruch surface of degree 2 (a special weak del Pezzo surface )\, to the extent it is understood by Orlov and Kuleshov for del Pezzo sur faces.\n (1) First\, we prove that for any exceptional object in it\, one can find an autoequivalence which sends it to an exceptional vector bundle .\nThis result was conjectured by Shinnosuke Okawa and the speaker in 2015 .\n (2) Refining the method of the proof of the above result\, and based o n a deformation argument\, we prove that the braid group on 4 strands acts transitively (up to shifts) on the set of exceptional collections of leng th 4. This is a special case of an old conjecture by Bondal and Polishchuk .\n (3) We also prove that any exceptional collection can be extended to a full exceptional collection.\nMy talk is based on a joint work with Shinn osuke Okawa (Osaka) and Akira Ishii (Nagoya).\n LOCATION:https://researchseminars.org/talk/ZAG/80/ END:VEVENT END:VCALENDAR