Numerical trivial foliations, Iitaka Fibrations and the numerical dimension

Abstract

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.