Given a projective algebraic variety and a line bundle , the Kodaira-Itaka dimension of is defined to be the supremum of the dimensions of the image of by the map associated to the linear system , when is a positive integer, namely
It is a standard fact that if we consider the graded ring
When the line bundle we have is the canonical bundle of , then its Kodaira-Itaka dimension is called Kodaira dimension of .
In paticular, if for some we have then and is called big.
If , then is said to be of general type.
|Date of creation||2013-03-22 16:12:43|
|Last modified on||2013-03-22 16:12:43|
|Last modified by||yark (2760)|