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In mathematics, in the field of algebraic geometry, the period mapping relates families of Kähler manifolds to families of Hodge structures. == Ehresmann's theorem == (詳細はEhresmann's theorem guarantees that there is a small open neighborhood ''U'' around 0 in which ''f'' becomes a fiber bundle. That is, is diffeomorphic to . In particular, the composite map : is a diffeomorphism. This diffeomorphism is not unique because it depends on the choice of trivialization. The trivialization is constructed from smooth paths in ''U'', and it can be shown that the homotopy class of the diffeomorphism depends only on the choice of a homotopy class of paths from ''b'' to 0. In particular, if ''U'' is contractible, there is a well-defined diffeomorphism up to homotopy. The diffeomorphism from ''X''''b'' to ''X''0 induces an isomorphism of cohomology groups : and since homotopic maps induce identical maps on cohomology, this isomorphism depends only on the homotopy class of the path from ''b'' to 0. 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「period mapping」の詳細全文を読む スポンサード リンク
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