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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 Bott–Samelson resolution ： ウィキペディア英語版 Bott–Samelson resolution In algebraic geometry, the Bott–Samelson resolution of a Schubert variety is a resolution of singularities. It was introduced by in the context of compact Lie groups. The algebraic formulation is due to and . == Definition == Let ''G'' be a connected reductive complex algebraic group, ''B'' a Borel subgroup and ''T'' a maximal torus contained in ''B''. Let $w\; \backslash in\; W\; =\; N\_G(T)/T.$ Any such ''w'' can be written as a product of reflections by simple roots. Fix minimal such an expression: :$\backslash underline\; =\; (s\_,\; s\_,\; \backslash ldots,\; s\_)$ so that $w\; =\; s\_\; s\_\; \backslash cdots\; s\_$. (''l'' is the length of ''w''.) Let $P\_\; \backslash subset\; G$ be the subgroup generated by ''B'' and a representative of $s\_$. Let $Z\_\}\; =\; P\_\; \backslash times\; \backslash cdots\; \backslash times\; P\_/B^l$ with respect to the action of $B^l$ by :$(b\_1,\; \backslash ldots,\; b\_l)\; \backslash cdot\; (p\_1,\; \backslash ldots,\; p\_l)\; =\; (p\_1\; b\_1^,\; b\_1\; p\_2\; b\_2^,\; \backslash ldots,\; b\_\; p\_l\; b\_l^)$. It is a smooth projective variety. Writing $X\_w\; =\; \backslash overline\; /\; B\; =\; (P\_\; \backslash cdots\; P\_)/B$ for the Schubert variety for ''w'', the multiplication map :$\backslash pi:\; Z\_\_\; =\; \backslash mathcal\_$ and $R^i\; \backslash pi\_$ * \mathcal_ = 0, \, i \ge 1. In other words, $X\_w$ has rational singularities. There are also some other constructions; see, for example, . See also Bott–Samelson 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「Bott–Samelson resolution」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.