The abundance conjecture for Kähler log canonical pairs

Let $(X,\Delta)$ be a Kähler log canonical pair. A divisor is semiample if some positive multiple is base-point free. Abundance conjecture. If $K_X+\Delta$ is nef, then $K_X+\Delta$ is semiample.

The conjecture extends the projective abundance conjecture to Kähler varieties. It predicts that every minimal model admits a globally defined Iitaka fibration, which is important for the birational classification of algebraic varieties. The abundance conjecture is open in dimension at least $4$.