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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 vanishing theorem ： ウィキペディア英語版 Kodaira vanishing theorem In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices ''q'' > 0 are automatically zero. The implications for the group with index ''q'' = 0 is usually that its dimension — the number of independent global sections — coincides with a holomorphic Euler characteristic that can be computed using the Hirzebruch-Riemann-Roch theorem. == The complex analytic case == The statement of Kunihiko Kodaira's result is that if ''M'' is a compact Kähler manifold of complex dimension ''n'', ''L'' any holomorphic line bundle on ''M'' that is positive, and ''KM'' is the canonical line bundle, then :::$H^q(M,\; K\_M\backslash otimes\; L)\; =\; 0$ for ''q'' > 0. Here $K\_M\backslash otimes\; L$ stands for the tensor product of line bundles. By means of Serre duality, one also obtains the vanishing of $H^q(M,\; L^)$ for ''q'' < ''n''. There is a generalisation, the Kodaira-Nakano vanishing theorem, in which $K\_M\backslash otimes\; L\backslash cong\backslash Omega^n(L)$, where Ω''n''(''L'') denotes the sheaf of holomorphic (''n'',0)-forms on ''M'' with values on ''L'', is replaced by Ω''r''(''L''), the sheaf of holomorphic (r,0)-forms with values on ''L''. Then the cohomology group H''q''(''M'', Ω''r''(''L'')) vanishes whenever ''q'' + ''r'' > ''n''. 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 vanishing theorem」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.