  We propose a generalization of SHGH Conjectures to a smooth projective
surface Y: the so called Segre Problem. The study of linear systems on Y can be
translated in terms of the Mori cone of the blow up $X = Bl_r Y$ at $r$ general
points. Generalizing a result by de Fernex, we prove that if Segre Problem
holds true, then a part of the Mori cone of $X$ does coincide with a part of
the positive cone of $X$.
