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Okounkov bodies associated to pseudoeffective divisors

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Title
Okounkov bodies associated to pseudoeffective divisors
Author(s)
Sung Rak Choi; Yoonsuk Hyun; Jinhyung Park; Joonyeong Won
Publication Date
2018-04
Journal
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, v.97, no., pp.170 - 195
Publisher
Wiley
Abstract
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–Mustat¸˘a 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.C.2018 London Mathematical Society
URI
https://pr.ibs.re.kr/handle/8788114/5455
ISSN
0024-6107
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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2018_JYW_Okounkov bodies associated to pseudoeffective divisors.pdfDownload

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