Okounkov bodies associated to pseudoeffective divisors

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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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
Volume97
Issue number2
DOIs
Publication statusPublished - 2018 Apr

Bibliographical note

Funding Information:
Received 18 August 2016; revised 5 July 2017; published online 8 February 2018. 2010 Mathematics Subject Classification 14C20 (primary), 52A20 (secondary). S. Choi and J. Park were partially supported by the NRF grant (NRF-2016R1C1B2011446). S. Choi was also supported in part by the Yonsei University Future-leading Research Initiative of 2017. J. Won was partially supported by IBS-R003-D1, Institute for Basic Science in Korea.

Publisher Copyright:
© 2018 London Mathematical Society

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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