Taiwanese Journal of Mathematics

Okounkov Bodies Associated to Pseudoeffective Divisors II

Sung Rak Choi, Jinhyung Park, and Joonyeong Won

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Abstract

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.

Article information

Source
Taiwanese J. Math., Volume 21, Number 3 (2017), 601-620.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874609

Digital Object Identifier
doi:10.11650/tjm/8097

Mathematical Reviews number (MathSciNet)
MR3661383

Zentralblatt MATH identifier
06871334

Subjects
Primary: 14C20: Divisors, linear systems, invertible sheaves

Keywords
Okounkov body pseudoeffective divisor asymptotic invariant Zariski decomposition

Citation

Choi, Sung Rak; Park, Jinhyung; Won, Joonyeong. Okounkov Bodies Associated to Pseudoeffective Divisors II. Taiwanese J. Math. 21 (2017), no. 3, 601--620. doi:10.11650/tjm/8097. https://projecteuclid.org/euclid.twjm/1498874609


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