General Type
Further information: General typeGeneral position is a property of configurations of points, or more generally other subvarieties (lines in general position, so no three concurrent, and the like) – it is an extrinsic notion, which depends on an embedding as a subvariety. Informally, subvarieties are in general position if they cannot be described more simply than others. An intrinsic analog of general position is general type, and corresponds to a variety which cannot be described by simpler polynomial equations than others. This is formalized by the notion of Kodaira dimension of a variety, and by this measure projective spaces are the most special varieties, though there are other equally special ones, meaning having negative Kodaira dimension. For algebraic curves, the resulting classification is: projective line, torus, higher genus surfaces, and similar classifications occur in higher dimensions, notably the Enriques–Kodaira classification of algebraic surfaces.
Read more about this topic: General Position
Famous quotes containing the words general and/or type:
“Some people are under the impression that all that is required to make a good fisherman is the ability to tell lies easily and without blushing; but this is a mistake. Mere bald fabrication is useless; the veriest tyro can manage that. It is in the circumstantial detail, the embellishing touches of probability, the general air of scrupulous—almost of pedantic—veracity, that the experienced angler is seen.”
—Jerome K. Jerome (1859–1927)
“One type of rice nourishes one hundred types of people.”
—Chinese proverb.