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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 Zariski's connectedness theorem ： ウィキペディア英語版 Zariski's connectedness theorem In algebraic geometry, Zariski's connectedness theorem says that under certain conditions the fibers of a morphism of varieties are connected. It is an extension of Zariski's main theorem to the case when the morphism of varieties need not be birational. Zariski's connectedness theorem gives a rigorous version of the "principle of degeneration" introduced by Enriques, which says roughly that a limit of absolutely irreducible cycles is absolutely connected. ==Statement== Suppose that ''f'' is a proper surjective morphism of varieties from ''X'' to ''Y'' such that the function field of ''Y'' is separably closed in that of ''X''. Then Zariski's connectedness theorem says that the inverse image of any normal point of ''Y'' is connected. An alternative version says that if ''f'' is proper and ''f'' * ''O''''X'' = ''O''''Y'', then ''f'' is surjective and the inverse image of any point of ''Y'' is connected. 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「Zariski's connectedness 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.