Local Numerical Equivalences and Okounkov Bodies in Higher Dimensions

Sung Rak Choi; Jinhyung Park; Joonyeong Won

doi:10.1307/mmj/20195797

Local Numerical Equivalences and Okounkov Bodies in Higher Dimensions

Sung Rak Choi, Jinhyung Park, Joonyeong Won

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	347-372
Number of pages	26
Journal	Michigan Mathematical Journal
Volume	71
Issue number	2
DOIs	https://doi.org/10.1307/mmj/20195797
State	Published - 2022

Bibliographical note

Funding 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.

Publisher Copyright:
© 2022 University of Michigan. All rights reserved.

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Cite this

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title = "Local Numerical Equivalences and Okounkov Bodies in Higher Dimensions",

abstract = "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 Ro{\'e}{\textquoteright}s work [R] on surfaces to higher-dimensional varieties although our proof is essentially different in nature.",

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doi = "10.1307/mmj/20195797",

language = "English",

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PY - 2022

Y1 - 2022

N2 - 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.

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Local Numerical Equivalences and Okounkov Bodies in Higher Dimensions

Abstract

Bibliographical note

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