algebraic variety

名词 n.
中文释义

英文释义

名词 n.
  1. 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 #92;mathcal#123;W#125; 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#92;in#92;mathcal#123;W#125; axe taken to be the germs of functions on #92;mathcal#123;W#125; induced by functions in the stalk #92;mathfrak#123;R#125;#95;x. 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,#92;mathfrak#123;R#125;), by definition, is a local-ringed space.

词形变化

algebraic varieties plural
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