Okounkov bodies associated to pseudoeffective divisors II
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-K\"{u}ronya-Lozovanu about the rational polyhedrality of Okounkov bodies of big divisors with finitely generated section rings.
Keywords
Cite
@article{arxiv.1608.00221,
title = {Okounkov bodies associated to pseudoeffective divisors II},
author = {Sung Rak Choi and Jinhyung Park and Joonyeong Won},
journal= {arXiv preprint arXiv:1608.00221},
year = {2017}
}
Comments
14 pages, deleted previous Section 5 and fixed several gaps in the previous version. to appear in Taiwanese J. Math. (special issue for the proceedings of the conference Algebraic Geometry in East Asia 2016)