V2EX normal variety

Normal Variety

释义 Definition

normal variety(常译:正规簇/正态簇):代数几何中的术语,指满足“正规性(normality)”条件的代数簇;直观上可理解为“奇点不太坏”、在代数上具有良好整性性质的一类几何对象。(在不同教材中也可能译作“正常簇”,但更常见为“正规簇”。)

发音 Pronunciation (IPA)

/nrml vrati/

例句 Examples

A normal variety has nice algebraic properties.
正规簇具有良好的代数性质。

In birational geometry, one often replaces a singular space by a normal variety to control functions and divisors more effectively.
在双有理几何中,人们常把带奇点的空间替换为正规簇,以便更有效地控制函数与因子(除子)。

词源 Etymology

normal 源自拉丁语 norma(“尺规、规范”),引申为“符合规范的”。variety 源自拉丁语 varietas(“多样性、变化”),在数学中被专门化为“由多项式方程定义的几何对象(簇)”。合起来 normal variety 即“满足正规性条件的簇”。

相关词 Related Words

文学与著作 Literary Works

  • Algebraic Geometry Robin Hartshorne(常在讨论正规性、整闭性与簇的局部性质时出现 normal variety
  • Basic Algebraic Geometry I. R. Shafarevich(介绍代数簇与正规性概念时频繁使用)
  • Principles of Algebraic Geometry Phillip Griffiths & Joseph Harris(在讲述复代数几何与奇点/除子理论背景时出现)
  • Introduction to Algebraic Geometry Serge Lang(基础理论章节中涉及正规簇/正规性相关表述)
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