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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 Rational singularity ： ウィキペディア英語版 Rational singularity In mathematics, more particularly in the field of algebraic geometry, a scheme $X$ has rational singularities, if it is normal, of finite type over a field of characteristic zero, and there exists a proper birational map :$f\; \backslash colon\; Y\; \backslash rightarrow\; X$ from a regular scheme $Y$ such that the higher direct images of $f\_$ * applied to $\backslash mathcal\_Y$ are trivial. That is, :$R^i\; f\_$ * \mathcal_Y = 0 for $i\; >\; 0$. If there is one such resolution, then it follows that all resolutions share this property, since any two resolutions of singularities can be dominated by a third. For surfaces, rational singularities were defined by . ==Formulations== Alternately, one can say that $X$ has rational singularities if and only if the natural map in the derived category :$\backslash mathcal\_X\; \backslash rightarrow\; R\; f\_$ * \mathcal_Y is a quasi-isomorphism. Notice that this includes the statement that $\backslash mathcal\_X\; \backslash simeq\; f\_$ * \mathcal_Y and hence the assumption that $X$ is normal. There are related notions in positive and mixed characteristic of * pseudo-rational and * F-rational Rational singularities are in particular Cohen-Macaulay, normal and Du Bois. They need not be Gorenstein or even Q-Gorenstein. Log terminal singularities are rational, 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「Rational singularity」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.