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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 Complex analytic space ： ウィキペディア英語版 Complex analytic space In mathematics, a complex analytic space is a generalization of a complex manifold which allows the presence of singularities. Complex analytic spaces are locally ringed spaces which are locally isomorphic to local model spaces, where a local model space is an open subset of the vanishing locus of a finite set of holomorphic functions. ==Definition== Denote the constant sheaf on a topological space with value $\backslash mathbb$ by $\backslash underline$-space is a locally ringed space $(X,\; \backslash mathcal\_X)$ whose structure sheaf is an algebra over $\backslash underline^n$, and fix finitely many holomorphic functions $f\_1,\backslash dots,f\_k$ in $U$. Let $X=V(f\_1,\backslash dots,f\_k)$ be the common vanishing locus of these holomorphic functions, that is, $X=\backslash$. Define a sheaf of rings on $X$ by letting $\backslash mathcal\_X$ be the restriction to $X$ of $\backslash mathcal\_U/(f\_1,\; \backslash ldots,\; f\_k)$, where $\backslash mathcal\_U$ is the sheaf of holomorphic functions on $U$. Then the locally ringed $\backslash mathbb$-space $(X,\; \backslash mathcal\_X)$ is a local model space. A complex analytic space is a locally ringed $\backslash mathbb$-space $(X,\; \backslash mathcal\_X)$ which is locally isomorphic to a local model space. Morphisms of complex analytic spaces are defined to be morphisms of the underlying locally ringed spaces, they are also called holomorphic maps. 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「Complex analytic space」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.