Asymptotic base loci via Okounkov bodies

Sung Rak Choi; Yoonsuk Hyun; Jinhyung Park; Joonyeong Won

doi:10.1016/j.aim.2017.11.007

Asymptotic base loci via Okounkov bodies

Sung Rak Choi, Yoonsuk Hyun, Jinhyung Park, Joonyeong Won

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	784-810
Number of pages	27
Journal	Advances in Mathematics
Volume	323
DOIs	https://doi.org/10.1016/j.aim.2017.11.007
Publication status	Published - 2018 Jan 7

Bibliographical note

Funding Information:
S. Choi and J. Park were partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) ( NRF-2016R1C1B2011446 ). J. Won was partially supported by IBS-R003-D1 , Institute for Basic Science in Korea .

Publisher Copyright:
© 2017 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1016/j.aim.2017.11.007

Cite this

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title = "Asymptotic base loci via Okounkov bodies",

abstract = "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.",

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AU - Choi, Sung Rak

AU - Hyun, Yoonsuk

AU - Park, Jinhyung

AU - Won, Joonyeong

N1 - Funding Information: S. Choi and J. Park were partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) ( NRF-2016R1C1B2011446 ). J. Won was partially supported by IBS-R003-D1 , Institute for Basic Science in Korea . Publisher Copyright: © 2017 Elsevier Inc.

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Y1 - 2018/1/7

N2 - 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.

AB - 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.

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ER -

Asymptotic base loci via Okounkov bodies

Abstract

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