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 ${\displaystyle X}$ with Kawamata log terminal singularities over a field ${\displaystyle k}$ if the canonical bundle ${\displaystyle K_{X}}$ is nef, then ${\displaystyle K_{X}}$ is semi-ample.

Important cases of the abundance conjecture have been proven by Caucher Birkar.^[1]