Abundance conjecture

In algebraic geometry, the abundance conjecture is a conjecture in birational geometry, more precisely in the minimal model program, stating that for every projective variety $$X$$ with Kawamata log terminal singularities over a field $$k$$ if the canonical bundle $$K_X$$ is nef, then $$K_X$$ is semi-ample.

Important cases of the abundance conjecture have been proven by Caucher Birkar.