For a nef line bundle $L$ on a normal projective variety $X$, we have three invariants- the nef dimension $n(L)$, the numerical dimension $\nu(L)$ and the Iitaka dimension $\kappa(L)$. $n(L)$ is realized as the dimension of the image of the nef reduction map of $L$ and $\kappa(L)$ as the dimension of the image of the Iitaka fibration of $L$. Is an analogous rational map defined for the numerical dimension $\nu(L)$ as well? Any comments, references or pointers welcome!
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