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Partial Okounkov bodies and toric geometry

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EMGW04 - K-stability and moment maps

Given a big line bundle L on a projective manifold, Lazarsfeld–Mustată and Kaveh–Khovanskii introduced method of constructing convex bodies associated with L. These convex bodies are known as Okounkov bodies. When L is endowed with a singular positive Hermitian metric h, I will explain how to construct smaller convex bodies from the data (L,h). These convex bodies play important roles in the study of the singularities of h. As an application, I will explain a non-trivial application in toric geometry due to Yi Yao.

This talk is part of the Isaac Newton Institute Seminar Series series.

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