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SUMMARY:Toric Slope Stability and Partial Bergman Kernels - Florian Pokorn
 y (KTH)
DTSTART:20120411T103000Z
DTEND:20120411T113000Z
UID:TALK36838@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:In this talk\, I will describe some recent work in collaborati
 on with Michael Singer.\n\nLet (L\, h) \\to (X\, \\omega) denote a polariz
 ed toric Kahler manifold. Fix a toric submanifold Y. We study the partial 
 density function corresponding to the partial Bergman kernel projecting sm
 ooth sections of L<sup>k</sup> onto holomorphic sections of L<sup>k</sup> 
 that vanish to order at least lk along Y for fixed l>0. I will explain how
  a distributional expansion of the partial density function (as k tends to
  infinity) can be used to give a direct proof that if \\omega has constant
  scalar curvature\, then (X\,L) must be slope semi-stable with respect to 
 Y. Finally\, we will discuss some extensions of this result.
LOCATION:MR2
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