Asymptotic base loci via Okounkov bodies

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An Okounkov body is a convex subset of Euclidean space associated to a divisor on a smooth projective variety with respect to an admissible flag. In this paper, we recover the asymptotic base loci from the Okounkov bodies by studying various asymptotic invariants such as the asymptotic valuations and the moving Seshadri constants. Consequently, we obtain the nefness and ampleness criteria of divisors in terms of the Okounkov bodies. Furthermore, we compute the divisorial Zariski decomposition by the Okounkov bodies, and find upper and lower bounds for moving Seshadri constants given by the size of simplexes contained in the Okounkov bodies. (C) 2017 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2018-01
Language
English
Article Type
Article
Citation

ADVANCES IN MATHEMATICS, v.323, pp.784 - 810

ISSN
0001-8708
DOI
10.1016/j.aim.2017.11.007
URI
http://hdl.handle.net/10203/295164
Appears in Collection
MA-Journal Papers(저널논문)
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