Seshadri constants and Okounkov bodies revisited

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Park, Jinhyung¹  Shin, Jaesun² 

[1] Sogang Univ, Dept Math, Seoul, South Korea

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon, South Korea

关键词: Seshadri constant;    Okounkov body;    Big divisor;    Filtered graded linear series;   

DOI  :  10.1016/j.jpaa.2020.106493

来源: Elsevier

【 摘 要 】

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]. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free