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 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 Shigeru Iitaka (1970, 1971).
In algebraic geometry, the Iitakadimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective...
Kodaira dimension of V. One can define an analogous ring for any line bundle L over V; the analogous dimension is called the Iitakadimension. A line...
University working in algebraic geometry who introduced the Kodaira dimension, and Iitakadimension. He was a world leader in the field of Algebraic geometry....
notation κ. Shigeru Iitaka extended it and defined the Kodaira dimension for higher dimensional varieties (under the name of canonical dimension), and later named...
Mumford in 1967 states that if L is a semi-ample invertible sheaf with Iitakadimension at least 2 on a complex projective manifold, then H i ( X , L − 1 )...
terminal" Kodaira dimension 1. The Kodaira dimension (also called the Iitakadimension) of a semi-ample line bundle L is the dimension of Proj of the section...
old problem of Iitaka on effectivity of Iitaka fibrations induced by pluri-canonical systems on varieties of non-negative Kodaira dimension. The problem...
(July 13–24, 1981). "What is known about the Hodge Conjecture?". In S. Iitaka (ed.). Advanced Studies in Pure Mathematics. Algebraic Varieties and Analytic...
Kawamata used analytic methods in Hodge theory to prove the Iitaka conjecture over a base of dimension 1. More recently, a series of papers by Kawamata related...
the holomorphic tangent bundle, that carried the basic data about the dimension of the moduli space, and obstructions to deformations. This theory is...
Graduate Texts in Mathematics. Vol. 52. Springer. ISBN 978-1-4757-3849-0. Iitaka, Shigeru (2011) [1982]. Algebraic Geometry: An Introduction to Birational...
space remains controversial owing to the aforementioned criticism raised by Iitaka. The infrared absorption spectra of ice XI was studied in 2009 in preparation...
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