Global Okounkov bodies for Bott-Samelson varieties

JOURNAL OF ALGEBRA

卷:490

Article

Schmitz, David¹  Seppaenen, Henrik² 

[1] Philipps Univ Marburg, Fachbereich Math & Informat, Hans Meerwein Str, D-35032 Marburg, Germany

[2] Georg August Univ Gottingen, Math Inst, Bunsenstr 3-5, D-37073 Gottingen, Germany

关键词: Bott-Samelson variety;    Mori dream space;    Linear series;    Okounkov body;   

DOI  :  10.1016/j.jalgebra.2017.07.018

来源: Elsevier

【 摘 要 】

We use the theory of Mori dream spaces 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 GIB is rational polyhedral. As an application we show that the asymptotic behaviour of dimensions of weight spaces in section spaces of line bundles is given by the volume of polytopes. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free