Global Okounkov bodies for Bott-Samelson varieties

David Schmitz, Henrik Seppänen

Published 2014-09-05Version 1

We use the theory of Mori dream spaces and GIT to prove that the global Okounkov body of a Bott-Samelson variety, with respect to a natural flag of subvarieties, is rational polyhedral. As a corollary, Okounkov bodies of effective line bundles over Schubert varieties are shown to be rational polyhedral. In particular, it follows that the global Okounkov body of a flag variety $G/B$ is rational polyhedral. As an application, we derive polyhedral expressions for the asymptotics of weight multiplicites in section spaces of line bundles.