A set on which the local Łojasiewicz exponent is attained

Jacek Chądzyński; Tadeusz Krasiński

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 3, page 297-301
  • ISSN: 0066-2216

Abstract

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Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping F = ( f ₁ , . . . , f ₘ ) : U → ℂ m , F(0) = 0, the Łojasiewicz exponent ₀(F) is attained on the set z ∈ U: f₁(z)·...·fₘ(z) = 0.

How to cite

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Jacek Chądzyński, and Tadeusz Krasiński. "A set on which the local Łojasiewicz exponent is attained." Annales Polonici Mathematici 67.3 (1997): 297-301. <http://eudml.org/doc/270377>.

@article{JacekChądzyński1997,
abstract = {Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping $F = (f₁,..., fₘ): U → ℂ^m$, F(0) = 0, the Łojasiewicz exponent ₀(F) is attained on the set z ∈ U: f₁(z)·...·fₘ(z) = 0.},
author = {Jacek Chądzyński, Tadeusz Krasiński},
journal = {Annales Polonici Mathematici},
keywords = {holomorphic mapping; Łojasiewicz exponent; polynomial mapping},
language = {eng},
number = {3},
pages = {297-301},
title = {A set on which the local Łojasiewicz exponent is attained},
url = {http://eudml.org/doc/270377},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Jacek Chądzyński
AU - Tadeusz Krasiński
TI - A set on which the local Łojasiewicz exponent is attained
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 3
SP - 297
EP - 301
AB - Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping $F = (f₁,..., fₘ): U → ℂ^m$, F(0) = 0, the Łojasiewicz exponent ₀(F) is attained on the set z ∈ U: f₁(z)·...·fₘ(z) = 0.
LA - eng
KW - holomorphic mapping; Łojasiewicz exponent; polynomial mapping
UR - http://eudml.org/doc/270377
ER -

References

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  1. [CK₁] J. Chądzyński and T. Krasiński, The Łojasiewicz exponent of an analytic mapping of two complex variables at an isolated zero, in: Singularities, S. Łojasiewicz (ed.), Banach Center Publ. 20, PWN, Warszawa, 1988, 139-146. Zbl0674.32004
  2. [CK₂] J. Chądzyński and T. Krasiński, A set on which the Łojasiewicz exponent at infinity is attained, Ann. Polon. Math. 67 (1997), 191-197. Zbl0924.32004
  3. [CK₃] J. Chądzyński and T. Krasiński, On the Łojasiewicz exponent for analytic curves, in: Singularities Symposium - Łojasiewicz 70, B. Jakubczyk, W. Pawłucki and J. Stasica (eds.), Banach Center Publ., to appear. Zbl0924.32006
  4. [LT] M. Lejeune-Jalabert et B. Teissier, Clôture intégrale des idéaux et equisingularité, Centre de Mathématiques, École Polytechnique, 1974. 
  5. [P] A. Płoski, Newton polygons and the Łojasiewicz exponent of a holomorphic mapping of ℂ², Ann. Polon. Math. 51 (1990), 275-281. Zbl0764.32012

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