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:
“... women can never do efficient and general service in hospitals until their dress is prescribed by laws inexorable as those of the Medes and Persians. Then, that dress should be entirely destitute of steel, starch, whale-bone, flounces, and ornaments of all descriptions; should rest on the shoulders, have a skirt from the waist to the ankle, and a waist which leaves room for breathing.”
—Jane Grey Swisshelm (1815–1884)
“It is not true that there is dignity in all work. Some jobs are definitely better than others.... People who have good jobs are happy, rich, and well dressed. People who have bad jobs are unhappy, poor and use meat extenders. Those who seek dignity in the type of work that compels them to help hamburgers are certain to be disappointed.”
—Fran Lebowitz (b. 1950)