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K-Stability and weighted K-stability

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If you have a question about this talk, please contact Dhruv Ranganathan.

Collins and Székelhyidi developed a notion of K-semistability for polarized affine cones and proved it is an obstruction for scalar-flat Kähler metrics to exist on the cone. In this talk, I will explain that Collins—Székelhyidi K-semistability coincides with the weighted K-semistability of the regular quotient whenever there is one and I will give evidence that the latter notion is finer. This is part of an ongoing joint work with Apostolov and Calderbank.

This talk is part of the Algebraic Geometry Seminar series.

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