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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 Smooth completion ： ウィキペディア英語版 Smooth completion In algebraic geometry, the smooth completion (or smooth compactification) of a smooth affine algebraic curve ''X'' is a complete smooth algebraic curve which contains ''X'' as an open subset.〔Griffiths, 1972, p. 286.〕 Smooth completions exist and are unique over a perfect field. ==Examples== An affine form of a hyperelliptic curve may be presented as $y^2=P(x)$ where $(x,\; y)\backslash in\backslash mathbb^2$ and () has distinct roots and has degree at least 5. The Zariski closure of the affine curve in $\backslash mathbb\backslash mathbb^2$ is singular at the unique infinite point added. Nonetheless, the affine curve can be embedded in a unique compact Riemann surface called its smooth completion. The projection of the Riemann surface to $\backslash mathbb\backslash mathbb^2$ is 2-to-1 over the singular point at infinity if $P(x)$ has even degree, and 1-to-1 (but ramified) otherwise. This smooth completion can also be obtained as follows. Project the affine curve to the affine line using the x-coordinate. Embed the affine line into the projective line, then take the normalization of the projective line in the function field of the affine curve. 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「Smooth completion」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.