Seshadri constants and Okounkov bodies revisited

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In recent years, the interaction between the local positivity of divisors and Okounkov bodies has attracted considerable attention, and there have been attempts to find a satisfactory theory of positivity of divisors in terms of convex geometry of Okounkov bodies. Many interesting results in this direction have been established by Choi- Hyun-Park-Won [4] and Kuronya-Lozovanu [17-19] separately. The first aim of this paper is to give uniform proofs of these results. Our approach provides not only a simple new outlook on the theory but also proofs for positive characteristic in the most important cases. Furthermore, we extend the theorems on Seshadri constants to graded linear series setting. Finally, we introduce the integrated volume function to investigate the relation between Seshadri constants and filtered Okounkov bodies introduced by Boucksom-Chen [3].
Publisher
ELSEVIER
Issue Date
2021-02
Language
English
Article Type
Article
Citation

JOURNAL OF PURE AND APPLIED ALGEBRA, v.225, no.2, pp.106493

ISSN
0022-4049
DOI
10.1016/j.jpaa.2020.106493
URI
http://hdl.handle.net/10203/281819
Appears in Collection
MA-Journal Papers(저널논문)
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