Local numerical equivalences and Okounkov bodies in higher dimensions.

We study what kind of local numerical properties of divisors is encoded in the Okounkov bodies. 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.