Kodaira dimension

Summary

The Kodaira dimension of a smooth projective variety measures how fast the spaces of sections of the powers of its canonical bundle grow. It takes one of the values $-\infty, 0, 1, \dots, n$, where $n$ is the dimension of the variety. It is a birational invariant, and it is the first coarse invariant in the classification of varieties, as in the Enriques–Kodaira classification of surfaces. Varieties of maximal Kodaira dimension are said to be of general type.