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 construction using global sections
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.
