  Modifying the notion of numerically trivial foliation of a pseudo-effective
line bundle L introduced by the author in math.AG/0304312 it can be shown that
the leaves of this foliation have codimension bigger or equal to the numerical
dimension of L as defined by Boucksom, Demailly, Paun and Peternell,
math.AG/0405285. Furthermore, if the Kodaira dimension of L equals its
numerical dimension the Kodaira-Iitaka fibration is its numerically trivial
foliation. Both statements together yield a sufficient criterion for L not
being abundant.
