Iitaka Dimension

In algebraic geometry, the Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective space determined by L. This is 1 less than the dimension of the ring

The Iitaka dimension of L is always less than or equal to the dimension of X. If L is not effective, then its Iitaka dimension is defined to be (or sometimes −1).

Read more about Iitaka Dimension:  Big Line Bundles, Kodaira Dimension

Famous quotes containing the word dimension:

    Le Corbusier was the sort of relentlessly rational intellectual that only France loves wholeheartedly, the logician who flies higher and higher in ever-decreasing circles until, with one last, utterly inevitable induction, he disappears up his own fundamental aperture and emerges in the fourth dimension as a needle-thin umber bird.
    Tom Wolfe (b. 1931)