About: Milnor number

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In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued holomorphic function germ then the Milnor number of f, denoted μ(f), is either a nonnegative integer, or is infinite. It can be considered both a geometric invariant and an algebraic invariant. This is why it plays an important role in algebraic geometry and singularity theory.

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  • In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued holomorphic function germ then the Milnor number of f, denoted μ(f), is either a nonnegative integer, or is infinite. It can be considered both a geometric invariant and an algebraic invariant. This is why it plays an important role in algebraic geometry and singularity theory. (en)
  • 数学では、特にでは、ジョン・ウィラード・ミルナー(John Willard Milnor)の名前にちなんだミルナー数(Milner number)は、函数の芽(germ)の不変量である。 f を複素数に値をとる正則函数の芽とすると、f のミルナー数は μ(f) と書いてゼロかまたは正の整数であるか無限大の値をとる。ミルナー数は微分幾何学的な不変量とも考えられるし、代数幾何学的な不変量とも考えられる。これが何故、代数幾何学やで重要な役割を果たすのであろうか？ (ja)
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  • In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued holomorphic function germ then the Milnor number of f, denoted μ(f), is either a nonnegative integer, or is infinite. It can be considered both a geometric invariant and an algebraic invariant. This is why it plays an important role in algebraic geometry and singularity theory. (en)
  • 数学では、特にでは、ジョン・ウィラード・ミルナー(John Willard Milnor)の名前にちなんだミルナー数(Milner number)は、函数の芽(germ)の不変量である。 f を複素数に値をとる正則函数の芽とすると、f のミルナー数は μ(f) と書いてゼロかまたは正の整数であるか無限大の値をとる。ミルナー数は微分幾何学的な不変量とも考えられるし、代数幾何学的な不変量とも考えられる。これが何故、代数幾何学やで重要な役割を果たすのであろうか？ (ja)
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  • ミルナー数 (ja)
  • Milnor number (en)
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