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Abstract
We prove that the existence of a finite Minkowski basis for Okounkov bodies on a smooth projective variety with respect to an admissible flag implies the rational polyhedrality of the global Okounkov body. As an application of this general result, we deduce that the global Okounkov body of a surface with finitely generated pseudo-effective cone with respect to a general flag is rational polyhedral. We give an alternative proof for this fact which recovers the generators more explicitly. We also prove the rational polyhedrality of global Okounkov bodies in the case of certain homogeneous 3-folds using inductive methods.
Received: 2014-6-17
Revised: 2014-7-9
Published Online: 2016-1-16
Published in Print: 2016-1-1
© 2016 by Walter de Gruyter Berlin/Boston
