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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 GIT quotient ： ウィキペディア英語版 GIT quotient In algebraic geometry, an affine GIT quotient, or affine geometric invariant theory quotient, of an affine scheme $\backslash operatorname\; A$ with action by a group scheme ''G'' is the affine scheme $\backslash operatorname(A^G)$, the prime spectrum of the ring of invariants of ''A'', and is denoted by $X\; /\backslash !/\; G$. A GIT quotient is a categorical quotient: any invariant morphism uniquely factors through it. Taking Proj (of a graded ring) instead of $\backslash operatorname$, one obtains a projective GIT quotient (which is a quotient of the set of semistable points.) A GIT quotient is a categorical quotient (of the semistable points); i.e., "the" quotient. Since the categorical quotient is unique, if there is a geometric quotient, then the two notions coincide: for example, one has $G\; /\; H\; =\; G\; /\backslash !/\; H\; =\; \backslash operatornamek()^H$ for an algebraic group ''G'' over a field ''k'' and closed subgroup ''H''. If ''X'' is a complex smooth projective variety, then the GIT quotient of ''X'' by ''G'' is homeomorphic to the symplectic quotient of ''X'' by a maximal compact subgroup of ''G'' (Kempf–Ness theorem). == See also == *quotient stack *character variety 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「GIT quotient」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.