翻訳と辞書 Words near each other ・ Regulation of electronic cigarettes ・ Regulation of emotion ・ Regulation of Financial Services (Land Transactions) Act 2005 ・ Regulation of food and dietary supplements by the U.S. Food and Drug Administration ・ Regulation of gastric function ・ Regulation of gene expression ・ Regular clergy ・ Regular conditional probability ・ Regular constraint ・ Regular Democratic Organization ・ Regular Division of the Plane ・ Regular dodecahedron ・ Regular economy ・ Regular element ・ Regular element of a Lie algebra ・ Regular embedding ・ Regular expression ・ Regular extension ・ Regular Force ・ Regular Fries ・ Regular grammar ・ Regular Grand Lodge of Macedonia ・ Regular graph ・ Regular grid ・ Regular Guys ・ Regular Hadamard matrix ・ Regular haircut ・ Regular homotopy ・ Regular icosahedron ・ Regular ideal Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Regular embedding ： ウィキペディア英語版 Regular embedding In algebraic geometry, a closed immersion $i:\; X\; \backslash hookrightarrow\; Y$ of schemes is a regular embedding of codimension ''r'' if each point ''x'' in ''X'' has an open affine neighborhood ''U'' in ''Y'' such that the ideal of $X\; \backslash cap\; U$ is generated by a regular sequence of length ''r''. For example, if ''X'' and ''Y'' are smooth over a scheme ''S'' and if ''i'' is an ''S''-morphism, then ''i'' is a regular embedding. In particular, every section of a smooth morphism is a regular embedding. If $\backslash operatornameB$ is regularly embedded into a regular scheme, then ''B'' is a complete intersection ring. The notion is used, for instance, in an essential way in Fulton's approach to intersection theory. The important fact is that when ''i'' is a regular embedding, if ''I'' is the ideal sheaf of ''X'' in ''Y'', then the normal sheaf, the dual of $I/I^2$, is locally free (thus a vector bundle) and the natural map $\backslash operatorname(I/I^2)\; \backslash to\; \backslash oplus\_0^\backslash infty\; I^n/I^$ is an isomorphism: the normal cone $\backslash operatorname(\backslash oplus\_0^\backslash infty\; I^n/I^)$ coincides with the normal bundle. A flat morphism of finite type $f:X\; \backslash to\; Y$ is called a (local) complete intersection morphism if each point ''x'' in ''X'' has an open affine neighborhood ''U'' so that ''f'' |''U'' factors as $U\; \backslash overset\backslash to\; V\; \backslash overset\backslash to\; Y$ where ''j'' is a regular embedding and ''g'' is smooth. For example, if ''f'' is a morphism between smooth varieties, then ''f'' factors as $X\; \backslash to\; X\; \backslash times\; Y\; \backslash to\; Y$ where the first map is the graph morphism and so is a complete intersection morphism. == References == *, section B.7 *E. Sernesi: ''(Deformations of algebraic schemes )'' 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「Regular embedding」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.