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2021 Local Numerical Equivalences and Okounkov Bodies in Higher Dimensions
Sung Rak Choi, Jinhyung Park, Joonyeong Won
Michigan Math. J. Advance Publication 1-26 (2021). DOI: 10.1307/mmj/20195797

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.

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Sung Rak Choi. Jinhyung Park. Joonyeong Won. "Local Numerical Equivalences and Okounkov Bodies in Higher Dimensions." Michigan Math. J. Advance Publication 1 - 26, 2021. https://doi.org/10.1307/mmj/20195797

Information

Received: 9 September 2019; Revised: 7 August 2020; Published: 2021
First available in Project Euclid: 23 December 2020

Digital Object Identifier: 10.1307/mmj/20195797

Subjects:
Primary: 14C20 , 52A20

Rights: Copyright © 2021 The University of Michigan

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