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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 Kodaira–Spencer map ： ウィキペディア英語版 Kodaira–Spencer map In mathematics, the Kodaira–Spencer map, introduced by Kunihiko Kodaira and Donald C. Spencer, is a map associated to a deformation of a scheme or complex manifold ''X'', taking a tangent space of a point of the deformation space to the first cohomology group of the sheaf of vector fields on ''X''. == Definition == The Kodaira–Spencer map is :$\backslash delta:\; T\_0\; S\; \backslash to\; H^1(X,\; TX)$ where *$\backslash mathcal\; \backslash to\; S$ is a smooth proper map between complex spaces〔The main difference between a complex manifold and a complex space is that the latter is allowed to have a nilpotent.〕 (i.e., a deformation of the special fiber $X\; =\; \backslash mathcal\_0$.) *$\backslash delta$ is the connecting homomorphism obtained by taking a long exact cohomology sequence of the surjection $T\; \backslash mathcal|\_X\; \backslash to\; T\_0\; S\; \backslash otimes\; \backslash mathcal\_X$ whose kernel is the tangent bundle $TX$. If $v$ is in $T\_0\; S$, then its image $\backslash delta(v)$ is called the Kodaira–Spencer class of ''v''. The basic fact is: there is a natural bijection between isomorphisms classes of $\backslash mathcal\; \backslash to\; S\; =\; \backslash operatorname(\backslash mathbb()/t^2)$ and $H^1(X,\; TX)$. 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「Kodaira–Spencer map」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.