BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Karen Smith (University of Michigan)
DTSTART:20210513T203000Z
DTEND:20210513T220000Z
DTSTAMP:20260423T021331Z
UID:FOTR/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FOTR/50/">Ex
 tremal singularities in prime characteristic</a>\nby Karen Smith (Universi
 ty of Michigan) as part of Fellowship of the Ring\n\n\nAbstract\nWhat is t
 he most singular possible singularity? What can we say about it's geometri
 c and algebraic properties? This seemingly naive question has a sensible a
 nswer in characteristic p.  The "F-pure threshold\," which is an analog of
  the log canonical threshold\,  can be used to "measure" how bad a singula
 rity 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 poi
 nt (or more generally\, any F-pure point) but less than one in general\, w
 ith "more singular" points having smaller F-pure thresholds. We explain a 
 recently proved  lower bound on the F-pure threshold in terms of the multi
 plicity of the singularity. We also show that there is a nice class of hyp
 ersurfaces--which we call "Extremal hypersurfaces"---for which this bound 
 is achieved. These have very nice (extreme!) geometric properties. For exa
 mple\, the affine cone over a non Frobenius split cubic surface of charact
 eristic two is one example of an "extremal singularity". Geometrically\, t
 hese are the only cubic surfaces with the property that *every* triple of 
 coplanar lines on the surface meets in a single point (rather than a "tria
 ngle" as expected)--a very extreme property indeed.\n
LOCATION:https://researchseminars.org/talk/FOTR/50/
END:VEVENT
END:VCALENDAR