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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 . ==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 ''f'' *''L'' is a big line bundle on ''Y''. All ample line bundles are big. Big line bundles need not determine birational isomorphisms of ''X'' with its image. For example, if ''C'' is a hyperelliptic curve (such as a curve of genus two), then its canonical bundle is big, but the rational map it determines is not a birational isomorphism. Instead, it is a two-to-one cover of the canonical curve of ''C'', which is a rational normal curve. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Iitaka dimension」の詳細全文を読む スポンサード リンク
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