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.
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Received August 17, 2016; Accepted February 1, 2017. 2010 Mathematics Subject Classification. Primary 14C20; Secondary 52A20. Key words and phrases. Okounkov body, pseudoeffective divisor, asymptotic invariants of a divisor, Zariski decomposition. S. Choi and J. Park were partially supported by the NRF grant (NRF-2016R1C1B2011446). J. Won was partially supported by IBS-R003-D1, Institute for Basic Science in Korea.
© 2017 Korean Mathematial Soiety.
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