Iitaka
Shigeru Iitaka (飯高 茂 Iitaka Shigeru, born May 29, 1942, Chiba (city), Chiba) is a Japanese mathematician at Gakushuin University working in algebraic geometry who introduced the Kodaira dimension and Iitaka dimension. He was a worldly leader in the field of Algebraic geometry. He received in 1970 his Ph.D. from the University of Tokyo under Kunihiko Kodaira with thesis「代数多様体のD-次元について」(''On D-dimensions of algebraic varieties''). He was awarded the Iyanaga Prize of the Mathematical Society of Japan in 1980 and the Japan Academy Prize (academics), Japan Academy Prize in 1990. References External linksCV of Shigeru Iitaka
Living people 20th-century Japanese mathematicians 21st-century Japanese mathematicians Algebraic geometers 1942 births Gakushuin University faculty {{Japan-mathematician-stub ...
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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'' :R(X, L) = \bigoplus_^\infty H^0(X, 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 . Big line bundles A line bundle is big if it is of maximal Iitaka dimension, that is, if its Iitaka dimension is equal to the dimension of the underlying variety. Bigness is a birational invariant: If is a birational morphism of varieties, and if ''L'' is a big line bundle on ''X'', then ...
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