The abundance conjecture for smooth varieties

Let $X$ be a smooth variety with nef canonical divisor. Write $\kappa(X)$ for the Kodaira dimension of $X$ and $\nu(X)$ for the numerical dimension of its canonical divisor. Abundance conjecture. Then

$$\kappa(X)=\nu(X).$$

The conjecture asserts that the Kodaira and numerical dimensions agree for canonical divisors, extending the known partial results on abundance in algebraic geometry. Its general case remains open.