 Iitaka dimension

The Iitaka dimension of a Cartier divisor $D$ is the maximum dimension of the images of the rational maps given by its nonempty multiples $|mD|$. It is $-\infty$ if all positive multiples have no sections. For an integral $n$-dimensional projective variety it lies between zero and $n$ when nonnegative. The Kodaira dimension of the variety is the special case $D=K_X$.

The Iitaka dimension is a concept from algebraic geometry, specifically in the study of algebraic varieties and their properties. It is named after Shigeharu Iitaka, who introduced the notion. The Iitaka dimension of a projective variety (or more generally, a proper algebraic variety) is a measure of the growth rate of global sections of line bundles on the variety.