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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 Conic bundle ： ウィキペディア英語版 Conic bundle In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution of a Cartesian equation of the form : $X^2\; +\; aXY\; +\; b\; Y^2\; =\; P\; (T).\backslash ,$ Theoretically, it can be considered as a Severi–Brauer surface, or more precisely as a Châtelet surface. This can be a double covering of a ruled surface. Through an isomorphism, it can be associated with a symbol $(a,\; P)$ in the second Galois cohomology of the field $k$. In fact, it is a surface with a well-understood divisor class group and simplest cases share with Del Pezzo surfaces the property of being a rational surface. But many problems of contemporary mathematics remain open, notably (for those examples which are not rational) the question of unirationality. == A naive point of view == To write correctly a conic bundle, one must first reduce the quadratic form of the left hand side. Thus, after a harmless change, it has a simple expression like : $X^2\; -\; aY^2\; =\; P\; (T).\; \backslash ,$ In a second step, it should be placed in a projective space in order to complete the surface "at infinity". To do this, we write the equation in homogeneous coordinates and expresses the first visible part of the fiber : $X^2\; -\; aY^2\; =\; P\; (T)\; Z^2.\; \backslash ,$ That is not enough to complete the fiber as non-singular (clean and smooth), and then glue it to infinity by a change of classical maps: Seen from infinity, (i.e. through the change $T\backslash mapsto\; T\text{'}=\backslash frac\; 1\; T$), the same fiber (excepted the fibers $T\; =\; 0$ and $T\; \text{'}=\; 0$), written as the set of solutions $X\text{'}^2\; -\; aY\text{'}^2=\; P^$ * (T') Z'^2 where $P^$ * (T ') appears naturally as the reciprocal polynomial of $P$. Details are below about the map-change $(\text{'}:y\text{'}:\; z\; \text{'})$. 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「Conic 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.