Okounkov bodies and Zariski decompositions on surfaces
Bull. Korean Math. Soc. 2017 Vol. 54, No. 5, 1677-1697
Published online July 3, 2017
Printed September 30, 2017
Sung Rak Choi, Jinhyung Park, Joonyeong Won
Yonsei University, Korea Institute for Advanced Study, KAIST
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
MSC numbers : Primary 14C20; Secondary 52A20
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