Iitaka dimension

The m-pluricanonical map of complex manifolds M to W induces a fiber space structure.

The m-pluricanonical map is birational invariant. Pm(M)=Pm(W)

The existence of the birational map ψ :
Wm1 → Wm2 in the projective space

In algebraic geometry, the Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective space determined by L. This is 1 less than the dimension of the section ring of L

The Iitaka dimension of L is always less than or equal to the dimension of X. If L is not effective, then its Iitaka dimension is usually defined to be $-\infty$ or simply said to be negative (some early references define it to be −1). The Iitaka dimension of L is sometimes called L-dimension, while the dimension of a divisor D is called D-dimension. The Iitaka dimension was introduced by ShigeruIitaka (1970, 1971).

单词	Iitaka dimension
释义	Iitaka dimension 英语百科 Iitaka dimension In algebraic geometry, the Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective space determined by L. This is 1 less than the dimension of the section ring of L The Iitaka dimension of L is always less than or equal to the dimension of X. If L is not effective, then its Iitaka dimension is usually defined to be $-\infty$ or simply said to be negative (some early references define it to be −1). The Iitaka dimension of L is sometimes called L-dimension, while the dimension of a divisor D is called D-dimension. The Iitaka dimension was introduced by ShigeruIitaka (1970, 1971).
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