Kodaira-Iitaka Dimension on a Normal Prime Divisor

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, $Y\subset X$ an irreducible complete normal divisor and $\text{sL}$ an invertible sheaf on $X$, there exist integers $n_1>0,n_2\ge 0$ for which $\kappa (X,\text{sL})-1\le \kappa (Y,{\text{sL}}^{n_1}(-n_{2}Y){\mathrm{\mid }}_Y)$, where, if $Y$ is not a fixed component of large tensor powers of $\text{sL}$, we may take $n_1>>n_2$. This has implications for Kodaira-Iitaka dimension on a subvariety of any codimension.