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In commutative algebra, the multiplier ideal associated to a sheaf of ideals over a complex variety and a real number ''c'' consists (locally) of the functions ''h'' such that : is locally integrable, where the ''f''''i'' are a finite set of local generators of the ideal. Multiplier ideals were independently introduced by (who worked with sheaves over complex manifolds rather than ideals) and , who called them adjoint ideals. Multiplier ideals are discussed in the survey articles , , and . == Algebraic geometry == In algebraic geometry, the multiplier ideal of an effective -divisor measures singularities coming from the fractional parts of ''D'' so to allow one to prove vanishing theorems. Let ''X'' be a smooth complex variety and ''D'' an effective -divisor on it. Let be a log resolution of ''D'' (e.g., Hironaka's resolution). The multiplier ideal of ''D'' is : where is the relative canonical divisor: . It is an ideal sheaf of . If ''D'' is integral, then . 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「multiplier ideal」の詳細全文を読む スポンサード リンク
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