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
Famous quotes containing the words application to and/or application:
““Five o’clock tea” is a phrase our “rude forefathers,” even of the last generation, would scarcely have understood, so completely is it a thing of to-day; and yet, so rapid is the March of the Mind, it has already risen into a national institution, and rivals, in its universal application to all ranks and ages, and as a specific for “all the ills that flesh is heir to,” the glorious Magna Charta.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)