BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jarosław Buczyński (Polish Academy of Sciences) DTSTART:20220224T100000Z DTEND:20220224T110000Z DTSTAMP:20260423T005831Z UID:notts_ag/93 DESCRIPTION:Title: Fujita vanishing\, sufficiently ample line bundles\, and cactus varietie s\nby Jarosław Buczyński (Polish Academy of Sciences) as part of Onl ine Nottingham algebraic geometry seminar\n\n\nAbstract\nFor a fixed proje ctive manifold X\, we say that a property P(L) (where L is a line bundle o n X) is satisfied by sufficiently ample line bundles if there exists a lin e bundle M on X such that P(L) hold for any L with L-M ample. I will discu ss which properties of line bundles are satisfied by the sufficiently ampl e line bundles - for example\, can you figure out before the talk\, whethe r a sufficiently ample line bundle must be very ample? A basic ingredient used to study this concept is Fujita's vanishing theorem\, which is an ana logue of Serre's vanishing for sufficiently ample line bundles. At the end of the talk I will define cactus varieties (an analogue of secant varieti es) and sketch a proof that cactus varieties to sufficiently ample embeddi ngs of X are (set-theoretically) defined by minors of matrices with linear entries. The topic is closely related to conjectures of Eisenbud-Koh-Stil lman (for curves) and Sidman-Smith (for any varieties). The new ingredient s are based on a joint work in preparation with Weronika Buczyńska and Ł ucja Farnik.\n LOCATION:https://researchseminars.org/talk/notts_ag/93/ END:VEVENT END:VCALENDAR