A semiample divisor is a rational Cartier divisor 
for which some positive integral multiple
is Cartier and its associated line
bundle is generated by global sections. Equivalently, its sections have no common
zero and define a morphism to projective space.
An ample divisor is semiample, and the zero divisor is semiample. On a projective
variety every semiample divisor is nef, but nefness alone need not give semiampleness.
The definition also applies to actual holomorphic line bundles on compact complex spaces. A numerical class having a semiample representative
is a weaker condition than the given line bundle being
semiample. Log abundance concerns the particular adjoint divisor 
of a log canonical pair.
