Okounkov bodies and Zariski decompositions on surfaces

2016/03/02 by Sung Rak Choi, Jinhyung Park, Choi, Sung Rak +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1603.00618

openalex publication_date 2016/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to investigate the close relation between Okounkov bodies and Zariski decompositions of pseudoeffective divisors on smooth projective surfaces. Firstly, we completely determine the limiting Okounkov bodies on such surfaces, and give applications to Nakayama constants and Seshadri constants. Secondly, we study how the shapes of Okounkov bodies change as we vary the divisors in the big cone.

Cited by

• Newton-Okounkov bodies and normal toric degenerations

Related

• Minkowski decomposition of Okounkov bodies on surfaces
• Okounkov bodies associated to pseudoeffective divisors
• Okounkov bodies associated to pseudoeffective divisors II
• Local numerical equivalences and Okounkov bodies in higher dimensions
• Integral Zariski decompositions on smooth projective surfaces