Okounkov bodies associated to pseudoeffective divisors

Sung Rak Choi, Yoonsuk Hyun, Jinhyung Park, Joonyeong Won

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


An Okounkov body is a convex subset in Euclidean space associated to a big divisor on a smooth projective variety with respect to an admissible flag. In this paper, we introduce two convex bodies associated to pseudoeffective divisors, called the valuative Okounkov bodies and the limiting Okounkov bodies, and show that these convex bodies reflect the asymptotic properties of pseudoeffective divisors as in the case with big divisors. Our results extend the works of Lazarsfeld–Mustaţă and Kaveh–Khovanskii. For this purpose, we define and study special subvarieties, called the Nakayama subvarieties and the positive volume subvarieties, associated to pseudoeffective divisors.

Original languageEnglish
Pages (from-to)170-195
Number of pages26
JournalJournal of the London Mathematical Society
Issue number2
StatePublished - Apr 2018

Bibliographical note

Publisher Copyright:
© 2018 London Mathematical Society


  • 14C20 (primary)
  • 52A20 (secondary)


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