The generalized abundance conjecture predicts numerical semiampleness of a nef divisor 
on a projective Kawamata
log terminal pair when 
is pseudo-effective and 
is a nef Cartier divisor.
Numerical semiampleness means that a rational semiample
divisor on the same variety has the same intersection numbers with all integral
curves. It permits changing the numerically trivial part of the divisor. For example,
a nontorsion degree-zero line bundle on an elliptic
curve is nef and numerically equivalent to the trivial line
bundle but has no section in any positive power.
Analytic pseudo-effectivity of a real 
-class on a compact Kähler
manifold means that the class contains a closed positive 
-current.
