BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Krishna Hanumanthu (Chennai Mathematical Institute) DTSTART:20210622T110000Z DTEND:20210622T120000Z DTSTAMP:20260423T021446Z UID:ZAG/131 DESCRIPTION:Title: Ra tionality questions on Seshadri constants.\nby Krishna Hanumanthu (Che nnai Mathematical Institute) as part of ZAG (Zoom Algebraic Geometry) semi nar\n\n\nAbstract\nLet X be a projective variety and let L be an ample lin e bundle on X. For a point x in X\, the Seshadri constant of L at x is the infimum\, over all curves C passing through x\, of the ratios (L.C)/m\, w here (L.C) denotes the intersection product of L and C and m is the multip licity of C at x. These constants were defined by J.-P. Demailly in 1990 and they shed light on the local behaviour of L at x and even say somethin g about the nature of L and X. An important question about Seshadri const ants is whether they can be irrational. They are expected to be irrational often\, even though currently no examples are known. In this talk\, we wi ll focus on rational surfaces. We will discuss certain conjectures on line ar systems of plane curves and show that Seshadri constants of some ample line bundles are irrational if these conjectures are true. This talk is ba sed on joint works with B. Harbourne\, \\L. Farnik\, J. Huizenga\, D. Schm itz and T. Szemberg.\n LOCATION:https://researchseminars.org/talk/ZAG/131/ END:VEVENT END:VCALENDAR