Asymptotic base loci via Okounkov bodies

作者：Choi Sung Rak; Hyun Yoonsuk; Park Jinhyung^*; Won Joonyeong^*

来源：Advances in Mathematics, 2018, 323: 784-810.

DOI：10.1016/j.aim.2017.11.007

• Okounkov body
• Base locus
• Asymptotic valuation
• Zariski decomposition
• Seshadri constant

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.

• 出版日期2018-1-7