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A classical result in birational geometry, Mori’s Cone Theorem, implies that if the canonical bundle of a variety X is not nef then X contains rational curves. This is the starting point of the so-called Minimal Model Program. In particular, hyperbolic varieties are positive from the point of view of birational geometry. Very much in the same vein, one could ask what happens for a quasi projective variety, Y . Using resolution of singularity, then one is lead to consider pairs (X,D) of a variety and a divisor, such that Y = X \\ D. I will show how to obtain a theorem analogous to Mori’s Cone Theorem in this context. Instead of rational complete curves, algebraic copies of the complex plane will male their appearance. I will also discuss an ampleness criterion for hyperbolic pairs.\r\n