BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Karen Smith (University of Michigan) DTSTART:20210408T130000Z DTEND:20210408T140000Z DTSTAMP:20260423T035031Z UID:VCAS/76 DESCRIPTION:Title: Ex tremal Singularities in Prime Characteristic\nby Karen Smith (Universi ty of Michigan) as part of IIT Bombay Virtual Commutative Algebra Seminar\ n\n\nAbstract\nWhat is the most singular possible singularity? What can we say about its geometric and algebraic properties? This seemingly naive qu estion has a sensible answer in characteristic p.\nThe "F-pure threshold\, " which is an analog of the log canonical threshold\, can be used to "mea sure" how bad a singularity is. The F-pure threshold is a numerical invari ant 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 than one in general\, with "more singular" points having smaller F-pure th resholds. We explain a recently proved lower bound on the F-pure threshol d in 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!) geome tric properties. For example\, the affine cone over a non Frobenius split cubic surface of characteristic two is one example of an "extremal singula rity". Geometrically\, these are the only cubic surfaces with the property that *every* triple of coplanar lines on the surface meets in a single po int (rather than a "triangle" as expected)---a very extreme property indee d.\n LOCATION:https://researchseminars.org/talk/VCAS/76/ END:VEVENT END:VCALENDAR