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In mathematics, the canonical bundle of a non-singular algebraic variety of dimension over a field is the line bundle , which is the ''n''th exterior power of the cotangent bundle Ω on ''V''. Over the complex numbers, it is the determinant bundle of holomorphic ''n''-forms on ''V''. This is the dualising object for Serre duality on ''V''. It may equally well be considered as an invertible sheaf. The canonical class is the divisor class of a Cartier divisor ''K'' on ''V'' giving rise to the canonical bundle — it is an equivalence class for linear equivalence on ''V'', and any divisor in it may be called a canonical divisor. An anticanonical divisor is any divisor −''K'' with ''K'' canonical. The anticanonical bundle is the corresponding inverse bundle ω−1. When the anticanonical bundle of V is ample V is called Fano variety. ==The adjunction formula== (詳細はsmooth variety and that ''D'' is a smooth divisor on ''X''. The adjunction formula relates the canonical bundles of ''X'' and ''D''. It is a natural isomorphism : In terms of canonical classes, it is : This formula is one of the most powerful formulas in algebraic geometry. An important tool of modern birational geometry is inversion of adjunction, which allows one to deduce results about the singularities of ''X'' from the singularities of ''D''. 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「Canonical bundle」の詳細全文を読む スポンサード リンク
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