Multiplicity and the Łojasiewicz exponent

S. Spodzieja

Annales Polonici Mathematici (2000)

  • Volume: 73, Issue: 3, page 257-267
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Spodzieja, S.. "Multiplicity and the Łojasiewicz exponent." Annales Polonici Mathematici 73.3 (2000): 257-267. <http://eudml.org/doc/262772>.

@article{Spodzieja2000,
abstract = {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.},
author = {Spodzieja, S.},
journal = {Annales Polonici Mathematici},
keywords = {local Łojasiewicz exponent; holomorphic mapping; multiplicity},
language = {eng},
number = {3},
pages = {257-267},
title = {Multiplicity and the Łojasiewicz exponent},
url = {http://eudml.org/doc/262772},
volume = {73},
year = {2000},
}

TY - JOUR
AU - Spodzieja, S.
TI - Multiplicity and the Łojasiewicz exponent
JO - Annales Polonici Mathematici
PY - 2000
VL - 73
IS - 3
SP - 257
EP - 267
AB - 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.
LA - eng
KW - local Łojasiewicz exponent; holomorphic mapping; multiplicity
UR - http://eudml.org/doc/262772
ER -

References

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