Let X be a smooth complex projective variety and let L be a line bundle
on it. We describe the structure of the pre-polarized manifold (X,L) for non
integral values of the invariant ΟLβ(R):=βKXββ Ξ/(Lβ Ξ),
where Ξ is a minimal curve of an extremal ray R:=R+β[Ξ]
on X such that Lβ R>0.Comment: 13 page