Okounkov bodies associated to pseudoeffective divisors

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An Okounkov body is a convex subset in Euclidean space associated to a big divisor on a smooth projective variety with respect to an admissible flag. In this paper, we introduce two convex bodies associated to pseudoeffective divisors, called the valuative Okounkov bodies and the limiting Okounkov bodies, and show that these convex bodies reflect the asymptotic properties of pseudoeffective divisors as in the case with big divisors. Our results extend the works of Lazarsfeld-Mustata and Kaveh-Khovanskii. For this purpose, we define and study special subvarieties, called the Nakayama subvarieties and the positive volume subvarieties, associated to pseudoeffective divisors.
Publisher
WILEY
Issue Date
2018-04
Language
English
Article Type
Article
Citation

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, v.97, pp.170 - 195

ISSN
0024-6107
DOI
10.1112/jlms.12107
URI
http://hdl.handle.net/10203/295163
Appears in Collection
MA-Journal Papers(저널논문)
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