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 formula_1 with Kawamata log terminal singularities over a field formula_2 if the canonical bundle formula_3 is nef, then formula_3 is semi-ample.
Important cases of the abundance conjecture has been proved by Caucher Birkar. 