Filtrations and test-configurations

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• Gabor Szekelyhidi (Notre Dame)
• Wednesday 16 May 2012, 14:15-15:15
• MR 13, CMS.

If you have a question about this talk, please contact Caucher Birkar.

Test-configurations are certain degenerations of projective manifolds, which are used in the definition of K-stability, which in turn is related to the existence of special metrics. I will explain how filtrations of the homogeneous coordinate ring of a projective manifold can be thought of as sequences of test-configurations, and that they encode the limiting behavior of these sequences. Such filtrations arise naturally when studying the Calabi flow, or when trying to minimize the Calabi functional. I will also discuss how filtrations can be used to give a strengthening of the notion of K-stability, and why this is desirable.

This talk is part of the Algebraic Geometry Seminar series.

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