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Iitaka Fibration


An Iitaka fibration of a divisor of nonnegative Iitaka dimension is the rational fibration determined by its section-ratio field. For a rational Cartier divisor D on a normal integral projective variety over k, let

 V_m(D)=H^0(X,O_X(|_mD_|)),

where the floor function rounds each divisor coefficient down and the divisorial sheaf is reflexive. The Iitaka field K(D) subset= k(X) is generated by ratios of nonzero sections from the same V_m(D), over all positive integers m with V_m(D)!=0. In sufficiently large divisible degrees, the image of the complete system has this function field. Its dimension is kappa(X,D).


See also

Canonical Divisor, Iitaka Conjecture, Iitaka Dimension, Kodaira Dimension, Log Calabi-Yau Pair, Log Canonical Pair

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References

Birkar, C. "Lectures on Birational Geometry." 9 Oct 2012. https://arxiv.org/abs/1210.2670.

Cite this as:

Weisstein, Eric W. "Iitaka Fibration." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IitakaFibration.html

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