English Dictionary

algebraic variety

名詞

(algebraic geometry) The set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition.

日本語の意味

多項式方程式系（実数または複素数上）の解集合としての対象。 / 代数幾何学における、基本的かつ幾何的直観を保つように拡張された概念。

An algebraic variety defined by two polynomials can have singular points that complicate its topology.

2つの多項式方程式の解集合は、位相を複雑にする特異点を持つことがある。

意味（1）

(algebraic geometry) The set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition.

If 𝒲 is a locally closed subset (i.e., the intersection of open and closed sets) of an algebraic variety, it becomes an algebraic variety in a natural manner since the germs of regular functions at x∈𝒲 axe taken to be the germs of functions on 𝒲 induced by functions in the stalk Rₓ. The definitions of irreducibility and local rings of subvarieties for algebraic varieties are given in the same manner as before. From now on, by a variety is meant an algebraic variety. Any variety (X,R), by definition, is a local-ringed space.

algebraic varieties （ plural ）