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:
“The first general store opened on the ‘Cold Saturday’ of the winter of 1833 ... Mrs. Mary Miller, daughter of the store’s promoter, recorded in a letter: ‘Chickens and birds fell dead from their roosts, cows ran bellowing through the streets’; but she failed to state what effect the freeze had on the gala occasion of the store opening.”
—Administration in the State of Sout, U.S. public relief program (1935-1943)
“We need a type of theatre which not only releases the feelings, insights and impulses possible within the particular historical field of human relations in which the action takes place, but employs and encourages those thoughts and feelings which help transform the field itself.”
—Bertolt Brecht (1898–1956)