V2EX pluricanonical

Pluricanonical

释义 Definition

pluricanonical(复正则的/多重正则的):主要用于代数几何中,指与正则丛(canonical bundle)的某个正整数次幂相关的对象,尤其是指复正则线丛 \(K_X^{\otimes m}\)(\(m\ge 2\))及其截面、线性系或由此给出的映射(如 pluricanonical map,复正则映射)。也常用来修饰“divisor / system / map / form”等。

例句 Examples

A pluricanonical map can help distinguish different birational models of a surface.
复正则映射可以帮助区分曲面的不同双有理模型。

The theorem asserts that for sufficiently large \(m\), the pluricanonical linear system defines a birational embedding of the variety.
该定理断言当 \(m\) 足够大时,复正则线性系会给出该代数簇的一个双有理嵌入。

发音 Pronunciation (IPA)

/plriknnkl/

词源 Etymology

pluri-(“多个/多重”,源自拉丁语 plures “更多”)+ canonical(“正则的/典范的”,在代数几何里指与正则丛 \(K_X\) 相关)构成。整体含义即“与正则丛的多重(高次幂)有关的”。

相关词 Related Words

文学与著作 Literary Works

  • Algebraic Geometry Robin Hartshorne(常见于关于正则丛、线性系与映射的讨论中)
  • Principles of Algebraic Geometry Phillip Griffiths & Joseph Harris(涉及 canonical / pluricanonical 相关结构)
  • Positivity in Algebraic Geometry I & II Robert Lazarsfeld(大量出现 pluricanonical linear system 等术语)
  • Birational Geometry of Algebraic Varieties János Kollár & Shigefumi Mori(与极小模型纲领相关语境中常用)
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