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I will explain the construction of a pseudoeffective R-divisor Dλ on the blow-up of P3 at nine very general points which has negative intersections with an infinite set of curves, whose union is Zariski dense. ÌýIt follows that the diminished base locus B-(Dλ) = ∪A ample B(Dλ+A) is not closed and that Dλ does not admit a Zariski decomposition in even a very weak sense. ÌýAlong the way I will discuss some related examples, including an R-divisor which is nef on very general fibers of a family, but fails to be nef over countably many prime divisors in the base.