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-Küronya-Lozovanu about the rational polyhedrality of Okounkov bodies of big divisors with finitely generated section rings.

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)

Cited by in corpus (5)

• Okounkov bodies associated to abundant divisors and Iitaka fibrations
• Okounkov bodies and Zariski decompositions on surfaces
• Asymptotic base loci via Okounkov bodies
• Restricted volumes on Kähler manifolds
• Slices of Okounkov bodies of big divisors on Mori dream spaces