Toric Slope Stability and Partial Bergman Kernels (Florian Pokorny)

Duration: 38 mins 30 secs

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Created:

2012-04-24 09:31

Collection:

Workshop on Kahler Geometry

Publisher:

University of Cambridge

Dr J. Ross

Language:

eng (English)

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Author:

Florian Pokorny


Abstract:	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.

Abstract:

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.

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