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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 Hodge vector bundle ： ウィキペディア英語版 Hodge bundle In mathematics, the Hodge bundle, named after W. V. D. Hodge, appears in the study of families of curves, where it provides an invariant in the moduli theory of algebraic curves. Furthermore, it has applications to the theory of modular forms on reductive algebraic groups and string theory. ==Definitions== Let $\backslash mathcal\_g$ be the moduli space of algebraic curves of genus ''g'' curves over some scheme. The Hodge bundle Λ''g'' is a vector bundle on $\backslash mathcal\_g$ whose fiber at a point ''C'' in $\backslash mathcal\_g$ is the space of holomorphic differentials on the curve ''C''. To define the Hodge bundle, let $\backslash pi:\backslash mathcal\_g\backslash rightarrow\backslash mathcal\_g$ be the universal algebraic curve of genus ''g'' and let ω''g'' be its relative dualizing sheaf. The Hodge bundle is the pushforward of this sheaf, i.e. :$\backslash Lambda\_g=\backslash pi\_$ *\omega_g.\, 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「Hodge bundle」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.