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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 Quot scheme ： ウィキペディア英語版 Quot scheme In algebraic geometry, the Quot scheme is a scheme parametrizing locally free sheaves on a projective scheme. More specifically, if ''X'' is a projective scheme over a Noetherian scheme ''S'' and if ''F'' is a coherent sheaf on ''X'', then there is a scheme $\backslash operatorname\_F(X)$ whose set of ''T''-points $\backslash operatorname\_F(X)(T)\; =\; \backslash operatorname\_S(T,\; \backslash operatorname\_F(X))$ is the set of isomorphism classes of the quotients of $F\; \backslash times\_S\; T$ that are flat over ''T''. The notion was introduced by Alexander Grothendieck. It is typically used to construct another scheme parametrizing geometric objects that are of interest such as a Hilbert scheme. (In fact, taking ''F'' to be the structure sheaf $\backslash mathcal\_X$ gives a Hilbert scheme.) == References == *Nitsure, N. ''Construction of Hilbert and Quot schemes.'' Fundamental algebraic geometry: Grothendieck’s FGA explained, Mathematical Surveys and Monographs 123, American Mathematical Society 2005, 105–137. *https://amathew.wordpress.com/2012/06/02/the-stack-of-coherent-sheaves/ 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「Quot scheme」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.