We continue to explore the numerical nature of the Okounkov bodies focusing on the local behaviors near given points. More precisely, we show that the set of Okounkov bodies of a pseudoeffective divisor with respect to admissible flags centered at a fixed point determines the local numerical equivalence class of divisors, which is defined in terms of refined divisorial Zariski decompositions. Our results extend Roé’s work [R] on surfaces to higher-dimensional varieties although our proof is essentially different in nature.
|Number of pages||26|
|Journal||Michigan Mathematical Journal|
|Publication status||Published - 2022|
Bibliographical noteFunding Information:
S. Choi and J. Park were partially supported by the National Research Foundation of Korea (NRF-2016R1C1B2011446). J. Won was supported by the National Research Foundation of Korea (NRF-2020R1A2C1A01008018) and a KIAS Individual Grant (SP037003) via the Center for Mathematical Challenges at Korea Institute for Advanced Study.
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