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Cones and fibrations in the theory of K-stability

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If you have a question about this talk, please contact Joe Waldron .

The theory of K-stability is a tool for the study of uniformisation theorems on polarised varieties using methods of algebraic geometry. We introduce two new ideas into the theory. Relative K-stability attempts to classify degenerations of fibrations into three different types: degenerations of the cocycle, degenerations of the general fibre and degenerations of the base. We also extend the idea of working in a convex set of polarisations to the set of filtered graded linear series. The asymptotics of a filtration are described by real valued function on the Okounkov body of a polarisation. We describe the behaviour of this function as we move in the cone of filtered graded linear series.

This talk is part of the Junior Geometry Seminar series.

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