Kodaira-Itaka dimension
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
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.
Title | Kodaira-Itaka dimension |
---|---|
Canonical name | KodairaItakaDimension |
Date of creation | 2013-03-22 16:12:43 |
Last modified on | 2013-03-22 16:12:43 |
Owner | yark (2760) |
Last modified by | yark (2760) |
Numerical id | 17 |
Author | yark (2760) |
Entry type | Definition |
Classification | msc 14E05 |
Defines | Kodaira dimension |
Defines | bigness |
Defines | general type |