Newton-Okounkov Semigroups (are often not finitely generated)

Abstract: I will start with a combinatorialist's crash course on toric varieties which hopefully can be useful in its own right. After a short break, I will talk about Newton-Okounkov theory, which is an attempt to play as much of the toric game as possible with non-toric varieties. The theory associates an affine semigroup with a projectively embedded variety and tries to draw conlclusions from the asymptotic convex geometry of this semigroup. Many of these theorems assume that the semigroup is finitely generated, but checking finite generation seems to be hard. I will describe a combinatorial criterion, in a slightly non-toric situation (toric surface, but non-toric valuation), characterizing finite generation. This is joint work with Klaus Altmann, Alex Küronya, Karin Schaller & Lena Walter.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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