The Iitaka dimension 
of a line bundle 
on a projective variety 
is the maximum dimension
of the images of the rational maps defined by its nonempty complete
linear systems 
,
for positive integers 
.
It is 
when every positive power has no nonzero global section. For a rational Cartier
divisor 
,
one uses sufficiently divisible positive multiples of 
. The same definition applies to holomorphic line
bundles on compact complex manifolds.
For the trivial line bundle on a connected projective variety, the maps have point image and the Iitaka dimension is zero. For an ample
line bundle it equals 
. The Kodaira dimension
uses the canonical bundle, while the logarithmic
Kodaira dimension adds a reduced boundary divisor.
