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Multiplicity and the Łojasiewicz exponent

S. Spodzieja — 2000

Annales Polonici Mathematici

We give a formula for the multiplicity of a holomorphic mapping f : n Ω 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.

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