Partial Okounkov bodies and toric geometry

Abstract: 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.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html