Asymptotic base loci via Okounkov bodies

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


An Okounkov body is a convex subset of Euclidean space associated to a divisor on a smooth projective variety with respect to an admissible flag. In this paper, we recover the asymptotic base loci from the Okounkov bodies by studying various asymptotic invariants such as the asymptotic valuations and the moving Seshadri constants. Consequently, we obtain the nefness and ampleness criteria of divisors in terms of the Okounkov bodies. Furthermore, we compute the divisorial Zariski decomposition by the Okounkov bodies, and find upper and lower bounds for moving Seshadri constants given by the size of simplexes contained in the Okounkov bodies.

Original languageEnglish
Pages (from-to)784-810
Number of pages27
JournalAdvances in Mathematics
StatePublished - 7 Jan 2018

Bibliographical note

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© 2017 Elsevier Inc.


  • Asymptotic valuation
  • Base locus
  • Okounkov body
  • Seshadri constant
  • Zariski decomposition


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