Algebraic Geometry Seminar: "Newton-Okounkov bodies and measures of local positivity"

Abstract: Newton-Okounkov bodies are a convex-geometric way to understand the vanishing behaviour of global sections of line bundles in an asymptotic sense. While they have interesting connections with a variety of mathematical topics including representation theory, Diophantine approximation, and mathematical physics, here we will focus on their relationship with birational geometry. More specifically, we will see how they encode local positivity of line bundles and how they give rise to interesting invariants that are mostly unexplored even in the toric case.

Host: Ben Wormleighton