Kodaira dimension (awaiting review)

The Kodaira dimension of a projective variety $X$ with canonical bundle $K$ is the smallest integer $d$ such that the limit $$ \lim_{m \to \infty} \frac{H^0(X, K^{\otimes m})}{m^d} $$ exists and is non-zero. In the case no such integer exists, our convention is to take $d=-1$.