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http://dx.doi.org/10.4134/BKMS.b160686

OKOUNKOV BODIES AND ZARISKI DECOMPOSITIONS ON SURFACES  

Choi, Sung Rak (Department of Mathematics Yonsei University)
Park, Jinhyung (School of Mathematics Korea Institute for Advanced Study)
Won, Joonyeong (Department of Mathematical Sciences KAIST)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1677-1697 More about this Journal
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.
Keywords
Okounkov body; pseudoeffective divisor; asymptotic invariants of a divisor; Zariski decomposition;
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