Toric Slope Stability and Partial Bergman Kernels

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• Florian Pokorny (KTH)
• Wednesday 11 April 2012, 11:30-12:30
• MR2.

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 L^k onto holomorphic sections of L^k 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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