Abundance conjecture
# 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.

