The Kodaira dimension 
of a smooth projective variety is the Iitaka
dimension of its canonical bundle. Thus it
is the maximum dimension of the images of the pluricanonical
maps defined by 
for positive integers 
,
or 
if all these systems are empty. It is a birational invariant. A variety of dimension 
is of general type when its Kodaira
dimension equals 
.
A smooth projective curve has Kodaira dimension 
, zero, or one according as its genus is zero, one, or
at least two. A point has Kodaira dimension zero. The Iitaka
conjecture compares the Kodaira dimensions of a fiber
space, its base, and its general fiber.
