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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Relative canonical model ： ウィキペディア英語版 Relative canonical model In mathematics, the relative canonical model of a singular variety $X$ is a particular canonical variety that maps to $X$, which simplifies the structure. The precise definition is: If $f:Y\backslash to\; X$ is a resolution define the adjunction sequence to be the sequence of subsheaves $f\_$ *\omega_Y^; if $\backslash omega\_X$ is invertible $f\_$ *\omega_Y^=I_n\omega_X^ where $I\_n$ is the higher adjunction ideal. Problem. Is $\backslash oplus\_n\; f\_$ *\omega_Y^ finitely generated? If this is true then $Proj\; \backslash oplus\_n\; f\_$ *\omega_Y^ \to X is called the ''relative canonical model'' of $Y$, or the ''canonical blow-up'' of $X$.〔 Some basic properties were as follows: The relative canonical model was independent of the choice of resolution. Some integer multiple $r$ of the canonical divisor of the relative canonical model was Cartier and the number of exceptional components where this agrees with the same multiple of the canonical divisor of Y is also independent of the choice of Y. When it equals the number of components of Y it was called ''crepant''.〔 M. Reid, (Canonical 3-folds ) (courtesy copy), proceedings of the Angiers 'Journees de Geometrie Algebrique' 1979〕 It was not known whether relative canonical models were Cohen–Macaulay. Because the relative canonical model is independent of $Y$, most authors simplify the terminology, referring to it as the relative canonical model ''of '' $X$ rather than either the relative canonical model ''of '' $Y$ or the canonical blow-up of $X$. The class of varieties that are relative canonical models have canonical singularities. Since that time in the 1970s other mathematicians solved affirmatively the problem of whether they are Cohen–Macaulay. The minimal model program started by Shigefumi Mori proved that the sheaf in the definition always is finitely generated and therefore that relative canonical models always exist. ==References== 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「Relative canonical model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.