Multiplicity and the Łojasiewicz exponent

Volume 73 / 2000

S. Spodzieja Annales Polonici Mathematici 73 (2000), 257-267 DOI: 10.4064/ap-73-3-257-267


We give a formula for the multiplicity of a holomorphic mapping $f: ℂ^{n} ⊃ Ω → ℂ^{m}$, m > n, at an isolated zero, in terms of the degree of an analytic set at a point and the degree of a branched covering. We show that calculations of this multiplicity can be reduced to the case when m = n. We obtain an analogous result for the local Łojasiewicz exponent.


  • S. Spodzieja

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