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SUMMARY:Geoff Smith (UIC)
DTSTART;VALUE=DATE-TIME:20210507T190000Z
DTEND;VALUE=DATE-TIME:20210507T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T113053Z
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 Smithâ€™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/
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