BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Geoff Smith (UIC) DTSTART:20210507T190000Z DTEND:20210507T200000Z DTSTAMP:20260407T214607Z UID:agstanford/43 DESCRIPTION:Title: Normal bundles of rational curves and separably rationally connected v arieties\nby Geoff Smith (UIC) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nIn positive characteristic\, there are two differen t notions of rational connectedness: a variety can be rationally connected or separably rationally connected (SRC). SRC varieties share many of the nice properties that rationally connected varieties have in characteristic 0. But\, while it is conjectured that smooth Fano varieties are SRC\, it is only known that they are rationally connected. In the last decade\, sev eral mathematicians have come up with different ways to show that general Fano complete intersections are SRC. In this talk\, I'll explain this stor y\, and then discuss an approach Izzet Coskun and I are using to show that other sorts of varieties are SRC by comparing the normal bundle of a rati onal curve on a variety and its normal bundle to some subvariety containin g it. For instance\, I'll show that a Fano complete intersection of hypers urfaces each of degree at least 3 on a Grassmannian is SRC.\n\nThe discuss ion for Geoff Smith’s talk is taking place not in zoom-chat\, but at htt ps://tinyurl.com/2021-05-07-gs (and will be deleted after ~3-7 days).\n LOCATION:https://researchseminars.org/talk/agstanford/43/ END:VEVENT END:VCALENDAR