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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 Nash blowing-up ： ウィキペディア英語版 Nash blowing-up In algebraic geometry, a Nash blowing-up is a process in which, roughly speaking, each singular point is replaced by all the limiting positions of the tangent spaces at the non-singular points. Strictly speaking, if ''X'' is an algebraic variety of pure codimension ''r'' embedded in a smooth variety of dimension ''n'', $\backslash text(X)$ denotes the set of its singular points and $X\_\backslash text:=X\backslash setminus\; \backslash text(X)$ it is possible to define a map $\backslash tau:X\_\backslash text\backslash rightarrow\; X\backslash times\; G\_r^n$, where $G\_^$ is the Grassmannian of ''r''-planes in ''n''-space, by $\backslash tau(a):=(a,T\_)$, where $T\_$ is the tangent space of ''X'' at ''a''. Now, the closure of the image of this map together with the projection to ''X'' is called the Nash blowing-up of ''X''. Although (to emphasize its geometric interpretation) an embedding was used to define the Nash embedding it is possible to prove that it doesn't depend on it. ==Properties== * The Nash blowing-up is locally a monoidal transformation. * If ''X'' is a complete intersection defined by the vanishing of $f\_1,f\_2,\backslash ldots,f\_$ then the Nash blowing-up is the blowing-up with center given by the ideal generated by the (''n'' − ''r'')-minors of the matrix with entries $\backslash partial\; f\_i/\backslash partial\; x\_j$. * For a variety over a field of characteristic zero, the Nash blowing-up is an isomorphism if and only if ''X'' is non-singular. * For an algebraic curve over an algebraically closed field of characteristic zero the application of Nash blowings-up leads to desingularization after a finite number of steps. * In characteristic ''q'' > 0, for the curve $y^2-x^q=0$ the Nash blowing-up is the monoidal transformation with center given by the ideal $(x^)$, for ''q'' = 2, or $(y^2)$, for $q>2$. Since the center is a hypersurface the blowing-up is an isomorphism. Then the two previous points are not true in positive characteristic. 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「Nash blowing-up」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.