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SUMMARY:Karen Smith (University of Michigan)
DTSTART;VALUE=DATE-TIME:20201009T190000Z
DTEND;VALUE=DATE-TIME:20201009T200000Z
DTSTAMP;VALUE=DATE-TIME:20211209T071620Z
UID:agstanford/29
DESCRIPTION:Title: Extremal Singularities in Prime Characteristic\nby Karen Smith (Un
iversity of Michigan) as part of Stanford algebraic geometry seminar\n\n\n
Abstract\nWhat is the most singular possible singularity? What can we say
about its geometric and algebraic properties? This seemingly naive questio
n has a sensible answer in characteristic $p$.\nThe "F-pure threshold\," w
hich is an analog of the log canonical threshold\, can be used to "measur
e" how bad a singularity is. The F-pure threshold is a numerical invariant
of a point on (say) a hypersurface---a positive rational number that is
1 at any smooth point (or more generally\, any F-pure point) but less tha
n one in general\, with "more singular" points having smaller F-pure thres
holds. We explain a recently proved lower bound on the F-pure threshold i
n terms of the multiplicity of the singularity. We also show that there is
a nice class of hypersurfaces---which we call "Extremal hypersurfaces"---
for which this bound is achieved. These have very nice (extreme!) geometri
c properties. For example\, the affine cone over a non Frobenius split cub
ic surface of characteristic two is one example of an "extremal singularit
y". Geometrically\, these are the only cubic surfaces with the property th
at *every* triple of coplanar lines on the surface meets in a single point
(rather than a "triangle" as expected)---a very extreme property indeed.\
n\nThe discussion for Karen Smithâ€™s talk is taking place not in zoom-cha
t\, but at https://tinyurl.com/2020-10-09-ks (and will be deleted after ~
3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/29/
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