Okounkov bodies associated to pseudoeffective divisors II

Sung Rak Choi, Jinhyung Park, Joonyeong Won

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We first prove some basic properties of Okounkov bodies and give a characterization of Nakayama and positive volume subvarieties of a pseudoeffective divisor in terms of Okounkov bodies. Next, we show that each valuative and limiting Okounkov bodies of a pseudoeffective divisor which admits the birational good Zariski decomposition is a rational polytope with respect to some admissible flag. This is an extension of the result of Anderson-Küronya-Lozovanu about the rational polyhedrality of Okounkov bodies of big divisors with finitely generated section rings.

Original languageEnglish
Pages (from-to)601-620
Number of pages20
JournalTaiwanese Journal of Mathematics
Issue number3
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017, Mathematical Society of the Rep. of China. All rights reserved.


  • Asymptotic invariant
  • Okounkov body
  • Pseudoeffective divisor
  • Zariski decomposition


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