Let $X$ be a smooth simply connected projective variety of dimension $n$ (over complex numbers of course). For such $X$ we have two famous cones which are cone of effective curves and ample cone and are dual to each other.
Question: Is there any thing as Cone of effective divisors? Is there any problem to define such a thing? Has any body studied that? For surfaces, it is just cone of effective curves. So the smallest dimension at which we would get some thing new is three.