General Type
A variety of general type V is one of maximal Kodaira dimension (Kodaira dimension equal to its dimension):
Equivalently, K is a big line bundle; equivalently, the n-canonical map is generically injective for n sufficiently large.
For example, a variety with ample canonical bundle is of general type.
In some sense varieties of general type are generic, hence the term (discrete invariants of varieties of general type vary in more dimensions, and moduli space of varieties of general type have more dimensions; this is made more precise for curves and surfaces). A smooth hypersurface of degree d in the n-dimensional projective space is of general type if and only if d is greater than n+1. In this sense most smooth hypersurfaces in the complex projective space are of general type.
Varieties of general type seem too complicated to classify explicitly, even for surfaces.
Siu (1998) proved invariance of plurigenera under deformations for varieties of general type.
Read more about this topic: Kodaira Dimension
Famous quotes containing the words general and/or type:
“I never saw any people who appeared to live so much without amusement as the Cincinnatians.... Were it not for the churches,... I think there might be a general bonfire of best bonnets, for I never could discover any other use for them.”
—Frances Trollope (1780–1863)
“The type of fig leaf which each culture employs to cover its social taboos offers a twofold description of its morality. It reveals that certain unacknowledged behavior exists and it suggests the form that such behavior takes.”
—Freda Adler (b. 1934)