1Yonsei University, Seoul, South Korea 2Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea 3Ewha Womans University, Seoul, South Korea
Documenta mathematica, Tome 30 (2025) no. 5, pp. 1023-1053
The aim of this paper is to study the Okounkov bodies associated to abundant divisors. As a main result, we prove that the valuative Okounkov bodies of an abundant divisor encode all the numerical properties. We apply this result to recover the asymptotic base loci of an abundant divisor from the valuative Okounkov bodies. We also give a criterion for when the valuative and limiting Okounkov bodies of an abundant divisor coincide by comparing their Euclidean volumes. To obtain these results, we prove some variants of Fujita’s approximations for Okounkov bodies using Iitaka fibrations.
Sung Rak Choi
1
;
Jinhyung Park
2
;
Joonyeong Won
3
1
Yonsei University, Seoul, South Korea
2
Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea
3
Ewha Womans University, Seoul, South Korea
Sung Rak Choi; Jinhyung Park; Joonyeong Won. Okounkov bodies associated to abundant divisors and Iitaka fibrations. Documenta mathematica, Tome 30 (2025) no. 5, pp. 1023-1053. doi: 10.4171/dm/1021
@article{10_4171_dm_1021,
author = {Sung Rak Choi and Jinhyung Park and Joonyeong Won},
title = {Okounkov bodies associated to abundant divisors {and~Iitaka} fibrations},
journal = {Documenta mathematica},
pages = {1023--1053},
year = {2025},
volume = {30},
number = {5},
doi = {10.4171/dm/1021},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/1021/}
}
TY - JOUR
AU - Sung Rak Choi
AU - Jinhyung Park
AU - Joonyeong Won
TI - Okounkov bodies associated to abundant divisors and Iitaka fibrations
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DO - 10.4171/dm/1021
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