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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 Fermat curve ： ウィキペディア英語版 Fermat curve In mathematics, the Fermat curve is the algebraic curve in the complex projective plane defined in homogeneous coordinates (''X'':''Y'':''Z'') by the Fermat equation :$X^n\; +\; Y^n\; =\; Z^n.\backslash$ Therefore, in terms of the affine plane its equation is :$x^n\; +\; y^n\; =\; 1.\backslash$ An integer solution to the Fermat equation would correspond to a nonzero rational number solution to the affine equation, and vice versa. But by Fermat's last theorem it is now known that (for ''n'' ≥ 3) there are no nontrivial integer solutions to the Fermat equation; therefore, the Fermat curve has no nontrivial rational points. The Fermat curve is non-singular and has genus :$(n\; -\; 1)(n\; -\; 2)/2.\backslash$ This means genus 0 for the case ''n'' = 2 (a conic) and genus 1 only for ''n'' = 3 (an elliptic curve). The Jacobian variety of the Fermat curve has been studied in depth. It is isogenous to a product of simple abelian varieties with complex multiplication. The Fermat curve also has gonality :$n-1.\backslash$ ==Fermat varieties== Fermat-style equations in more variables define as projective varieties the Fermat varieties. 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「Fermat curve」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.