This is the second in a sequence of papers on the geometry of spaces of rational curves of degree e on a general hypersurface X ⊂ Pn of degree d. In [11] it is proved that if d < n+1 2 then for each e the space of rational curves is irreducible, reduced and has the expected dimension. In this paper it is proved that if d2 + d + 1 ≤ n, then for each e the… (More)