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Currently displaying 1 – 3 of 3

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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 $f : ℂ^{n} \supset Ω \to ℂ^{m}$ , 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.

The Lojasiewicz exponent at infinity for overdetermined polynomial mappings

S. Spodzieja — 2002

Annales Polonici Mathematici

We prove that the study of the Łojasiewicz exponent at infinity of overdetermined polynomial mappings $ℂ ⁿ \to ℂ^{m}$ , m > n, can be reduced to the one when m = n.

A characterization of proper regular mappings

T. Krasiński; S. Spodzieja — 2001

Annales Polonici Mathematici

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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