2014/09/06 by Henrik Seppänen, Seppänen, Henrik
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.1409.2026
supersedes the preprint arXiv:1007.1915
arxiv created 2014/09/06 · openalex publication_date 2014/09/06 · arxiv updated 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathscrL → X be an ample line bundle over a complex normal projective variety X. We construct a flag X0 ⊆ X1 ⊆ ⋯ ⊆ Xn=X of subvarieties for which the associated Okounkov body for \mathscrL is a rational polytope. In the case when X is a homogeneous surface, and the pseudoeffective cone of X is rational polyhedral, we also show that the global Okounkov body is a rational polyhedral cone if the flag of subvarieties is suitably chosen. Finally, we provide an application to the asymptotic study of group representations.