The numerical Abundance Conjecture

Let $X$ be a non-uniruled smooth complex projective variety. The numerical dimension of a pseudoeffective divisor $D$ is denoted by $u_X(D)$, and $u(X):= u_X(K_X)$, where $K_X$ is the canonical divisor; $\kappa(X)$ denotes the Kodaira dimension of $K_X$.

Abundance Conjecture. For every such $X$,

$$\nu(X):=\nu_X(K_X)=\kappa(X).$$

The result compares the numerical and Kodaira dimensions of the canonical divisor and is the numerical formulation of abundance for non-uniruled smooth projective varieties. The supplied text gives no resolution status for this formulation.