  This paper was inspired by work by T. Peternell, M. Schneider and A.J.
Sommese on the Kodaira dimension of subvarieties. In it I find a relation
between the Kodaira-Iitaka dimension of a divisor on a normal variety and that
of related divisors on an irreducible normal subvariety of codimension one. The
main result may be stated in a simplified form as: For $X$ a complete normal
variety, $Y \sub X$ an irreducible complete normal divisor and $\sL$ an
invertible sheaf on $X$, there exist integers $n_1 > 0, n_2 \geq 0$ for which
$\kappa(X,\sL) - 1 \leq \kappa(Y,\sL^{n_1}(-n_2Y)|_Y)$, where, if $Y$ is not a
fixed component of large tensor powers of $\sL$, we may take $n_1 >> n_2$. This
has implications for Kodaira-Iitaka dimension on a subvariety of any
codimension.

Algebraic Geometry