Application To Classification
The Iitaka conjecture states that the Kodaira dimension of a fibration is at least the sum of the Kodaira dimension of the base and the Kodaira dimension of a general fiber. This motivates a classification programme for algebraic varieties, in which it is sought to represent V as a fibration over a variety of general type, with typical fiber of Kodaira dimension 0. This is quite a natural idea, given that the application of the Proj construction to the pluricanonical ring should produce a projective variety in which the sections of powers of K 'capture' as much as they can about V.
Read more about this topic: Kodaira Dimension
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