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Local numerical equivalences and Okounkov bodies in higher dimensions (1808.02226v2)
Published 7 Aug 2018 in math.AG
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}'s work on surfaces to higher dimensional varieties although our proof is essentially different in nature.