The local multiplicity of a holomorphic map
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It is proved in this Chapter that the algebraic multiplicity of a holomorphic map coincides with its geometric multiplicity, that is with the index of the singular point of the corresponding holomorphic field. Although this result was known classically it seems that a detailed proof was published only in the paper  of V. P. Palamodov. The idea of the elementary proof presented below is due to A. G. Kushnirenko .
KeywordsBilinear Form Finite Type Local Algebra Trace Theorem Source Space
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