翻訳と辞書 Words near each other ・ Rational Service Tester for SOA Quality ・ Rational set ・ Rational sieve ・ Rational singularity ・ Rational Software ・ Rational Software Architect ・ Rational Software Modeler ・ Rational solution for Collaborative Lifecycle Management ・ Rational surface ・ Rational Synergy ・ Rational Tau ・ Rational Team Concert ・ Rational temperament ・ Rational trigonometry ・ Rational Unified Process ・ Rational variety ・ Rational Youth ・ Rational Youth (EP) ・ Rational zeta series ・ Rational-legal authority ・ Rationale ・ Rationale (clothing) ・ Rationale for gifted programs ・ Rationale for the Iraq War ・ Rationale of the Dirty Joke ・ Rationalis ・ Rationalisation (mathematics) ・ Rationalism ・ Rationalism (architecture) ・ Rationalism (disambiguation) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Rational variety ： ウィキペディア英語版 Rational variety In mathematics, a rational variety is an algebraic variety, over a given field ''K'', which is birationally equivalent to a projective space of some dimension over ''K''. This means that its function field is isomorphic to :$K(U\_1,\; \backslash dots\; ,\; U\_d),$ the field of all rational functions for some set $\backslash$ of indeterminates, where ''d'' is the dimension of the variety. ==Rationality and parameterization== Let ''V'' be an affine algebraic variety of dimension ''d'' defined by a prime ideal ''I''=⟨''f''1, ..., ''f''''k''⟩ in $K(\backslash dots\; ,\; X\_n)$. If ''V'' is rational, then there are ''n''+1 polynomials ''g''0, ..., ''g''''n'' in $K(U\_1,\; \backslash dots\; ,\; U\_d)$ such that $f\_i(g\_1/g\_0,\; \backslash ldots,\; g\_n/g\_0)=0.$ In order words, we have a rational parameterization $x\_i=\backslash frac(u\_1,\backslash ldots,u\_d)$ of the variety. Conversely, such a rational parameterization induces a field homomorphism of the field of functions of ''V'' into $K(U\_1,\; \backslash dots\; ,\; U\_d)$. But this homomorphism is not necessarily onto. If such a parameterization exists, the variety is said unirational. Lüroth's theorem (see below) implies that unirational curves are rational. Castelnuovo's theorem implies also that, in characteristic zero, every unirational surface is rational. 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「Rational variety」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.