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We give a formula for the multiplicity of a holomorphic mapping , 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.
We prove that the study of the Łojasiewicz exponent at infinity of overdetermined polynomial mappings , m > n, can be reduced to the one when m = n.
Let X, Y be complex affine varieties and f:X → Y a regular mapping. We prove that if dim X ≥ 2 and f is closed in the Zariski topology then f is proper in the classical topology.
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