2017/11/17 by Sung Rak Choi, Jinhyung Park, Choi, Sung Rak +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1711.07352
The aim of this paper is to study the Okounkov bodies associated to abundant divisors. As a main result, we prove that the valuative Okounkov bodies of an abundant divisor encode all the numerical properties. We apply this result to recover the asymptotic base loci of an abundant divisor from the valuative Okounkov bodies. We also give a criterion of when the valuative and limiting Okounkov bodies of an abundant divisor coincide by comparing their Euclidean volumes. To obtain these results, we prove some variants of Fujita's approximations for Okounkov bodies using Iitaka fibrations.