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Given a projective hyper-Kähler manifold Formula: see text, we study the asymptotic base loci of big divisors on Formula: see text. We provide a numerical characterization of these loci and study how they vary while moving a big divisor class in the big cone, using the divisorial Zariski decomposition, and the Beauville–Bogomolov–Fujiki form. We determine the dual of the cones of Formula: see text-ample divisors Formula: see text, for any Formula: see text, answering affirmatively (in the case of projective hyper-Kähler manifolds) a question asked by Sam Payne. We provide a decomposition for the effective cone Formula: see text into chambers of Mori-type, analogous to that for Mori dream spaces into Mori chambers. To conclude, we illustrate our results with several examples.
Denisi et al. (Fri,) studied this question.