TY - JOUR
T1 - Asymptotic base loci via Okounkov bodies
AU - Choi, Sung Rak
AU - Hyun, Yoonsuk
AU - Park, Jinhyung
AU - Won, Joonyeong
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2018/1/7
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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U2 - 10.1016/j.aim.2017.11.007
DO - 10.1016/j.aim.2017.11.007
M3 - Article
AN - SCOPUS:85033716087
VL - 323
SP - 784
EP - 810
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
ER -