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 with Kawamata log terminal singularities over a field if the canonical bundle is nef, then is semi-ample, i.e. is base-point free for some. In particular, if abundance holds, then one is able to define a model
Important cases of the abundance conjecture have been proven by Caucher Birkar.