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Toric Slope Stability and Partial Bergman Kernels

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  • UserFlorian Pokorny (KTH)
  • ClockWednesday 11 April 2012, 11:30-12:30
  • HouseMR2.

If you have a question about this talk, please contact Dr. J Ross.

In this talk, I will describe some recent work in collaboration with Michael Singer.

Let (L, h) \to (X, \omega) denote a polarized toric Kahler manifold. Fix a toric submanifold Y. We study the partial density function corresponding to the partial Bergman kernel projecting smooth sections of Lk onto holomorphic sections of Lk 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.

This talk is part of the Workshop on Kahler Geometry series.

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