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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 Pinch point (mathematics) ： ウィキペディア英語版 Pinch point (mathematics) In geometry, a pinch point or cuspidal point is a type of singular point on an algebraic surface. The equation for the surface near a pinch point may be put in the form :$f(u,v,w)\; =\; u^2\; -\; vw^2\; +\; ()\; \backslash ,$ where () denotes terms of degree 4 or more and $v$ is not a square in the ring of functions. For example the surface $1-2x+x^2-yz^2=0$ near the point $(1,0,0)$, meaning in coordinates vanishing at that point, has the form above. In fact, if $u=1-x,\; v=y$ and $w=z$ then is a system of coordinates vanishing at $(1,0,0)$ then $1-2x+x^2-yz^2=(1-x)^2-yz^2=u^2-vw^2$ is written in the canonical form. The simplest example of a pinch point is the hypersurface defined by the equation $u^2-vw^2=0$ called Whitney umbrella. The pinch point (in this case the origin) is a limit of normal crossings singular points (the $v$-axis in this case). These singular points are intimately related in the sense that in order to resolve the pinch point singularity one must blow-up the whole $v$-axis and not only the pinch point. ==See also== *Whitney umbrella *Singular point of an algebraic variety 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「Pinch point (mathematics)」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.