翻訳と辞書 Words near each other ・ Fourier optics ・ Fourier profilometry ・ Fourier ptychography ・ Fourier series ・ Fourier shell correlation ・ Fourier sine and cosine series ・ Fourier transform ・ Fourier transform infrared spectroscopy ・ Fourier transform ion cyclotron resonance ・ Fourier transform on finite groups ・ Fourier transform spectroscopy ・ Fourierism ・ Fourier–Bessel series ・ Fourier–Deligne transform ・ Fourier–Motzkin elimination ・ Fourier–Mukai transform ・ Fouriesburg ・ Fouriesburg Commando ・ Fourilles ・ Fourka ・ Fourka (disambiguation) ・ Fourmagnac ・ Fourmarierite ・ Fourme d'Ambert ・ Fourme de Montbrison ・ Fourmetot ・ Fourmidables (A'capella Quartet) ・ Fourmies ・ Fourmies, Nord ・ Fourmile Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fourier–Mukai transform ： ウィキペディア英語版 Fourier–Mukai transform In algebraic geometry, the Fourier–Mukai transform or Mukai–Fourier transform, introduced by , is an isomorphism between the derived categories of coherent sheaves on an abelian variety and its dual. It is analogous to the classical Fourier transform that gives an isomorphism between tempered distributions on a finite-dimensional real vector space and its dual. If the canonical class of a variety is positive or negative, then the derived category of coherent sheaves determines the variety. The Fourier–Mukai transform gives examples of different varieties (with trivial canonical bundle) that have isomorphic derived categories, as in general an abelian variety of dimension greater than 1 is not isomorphic to its dual. ==Definition== Let $X$ be an abelian variety and $\backslash hat\; X$ be its dual variety. We denote by $\backslash mathcal\; P$ the Poincaré bundle on :$X\; \backslash times\; \backslash hat\; X,$ normalized to be trivial on the fibers at zero. Let $p$ and $\backslash hat\; p$ be the canonical projections. The Fourier–Mukai functor is then :$R\backslash mathcal\; S:\; \backslash mathcal\; F\; \backslash in\; D(X)\; \backslash mapsto\; R\backslash hat\; p\_\backslash ast\; (p^\backslash ast\; \backslash mathcal\; F\; \backslash otimes\; \backslash mathcal\; P)\; \backslash in\; D(\backslash hat\; X)$ The notation here: ''D'' means derived category of coherent sheaves, and ''R'' is the higher direct image functor, at the derived category level. There is a similar functor :$R\backslash widehat\; :\; D(\backslash hat\; X)\; \backslash to\; D(X).\; \backslash ,$ 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「Fourier–Mukai transform」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.