A set on which the Łojasiewicz exponent at infinity is attained

Jacek Chądzyński; Tadeusz Krasiński

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 2, page 191-197
  • ISSN: 0066-2216

Abstract

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We show that for a polynomial mapping F = ( f ₁ , . . . , f ₘ ) : ℂ n → ℂ m the Łojasiewicz exponent ∞ ( F ) of F is attained on the set z ∈ ℂ n : f ₁ ( z ) · . . . · f ₘ ( z ) = 0 .

How to cite

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Jacek Chądzyński, and Tadeusz Krasiński. "A set on which the Łojasiewicz exponent at infinity is attained." Annales Polonici Mathematici 67.2 (1997): 191-197. <http://eudml.org/doc/270658>.

@article{JacekChądzyński1997,
abstract = {We show that for a polynomial mapping $F = (f₁,..., fₘ): ℂ^n → ℂ^m$ the Łojasiewicz exponent $_∞(F)$ of F is attained on the set $\{z ∈ ℂ^n: f₁(z) ·...· fₘ(z) = 0\}$.},
author = {Jacek Chądzyński, Tadeusz Krasiński},
journal = {Annales Polonici Mathematici},
keywords = {polynomial mapping; Łojasiewicz exponent; Łojasiewicz exponent at infinity},
language = {eng},
number = {2},
pages = {191-197},
title = {A set on which the Łojasiewicz exponent at infinity is attained},
url = {http://eudml.org/doc/270658},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Jacek Chądzyński
AU - Tadeusz Krasiński
TI - A set on which the Łojasiewicz exponent at infinity is attained
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 2
SP - 191
EP - 197
AB - We show that for a polynomial mapping $F = (f₁,..., fₘ): ℂ^n → ℂ^m$ the Łojasiewicz exponent $_∞(F)$ of F is attained on the set ${z ∈ ℂ^n: f₁(z) ·...· fₘ(z) = 0}$.
LA - eng
KW - polynomial mapping; Łojasiewicz exponent; Łojasiewicz exponent at infinity
UR - http://eudml.org/doc/270658
ER -

References

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  1. [BR] R. Benedetti and J. J. Risler, Real Algebraic and Semi-Algebraic Sets, Hermann, Paris, 1090. 
  2. [CK] J. Chądzyński and T. Krasiński, Exponent of growth of polynomial mappings of ℂ² into ℂ², in: Singularities, S. Łojasiewicz (ed.), Banach Center Publ. 20, PWN, Warszawa, 1988, 147-160. 
  3. [J] Z. Jelonek, Testing sets for properness of polynomial mappings, Inst. Math., Jagiellonian University, preprint 16 (1996), 37 pp. Zbl0946.14039
  4. [NZ] A. Némethi and A. Zaharia, Milnor fibration at infinity, Indag. Math. 3 (1992), 323-335. Zbl0806.57021
  5. [P₁] A. Płoski, Newton polygons and the Łojasiewicz exponent of a holomorphic mapping of ℂ², Ann. Polon. Math. 51 (1990), 275-281. Zbl0764.32012
  6. [P₂] A. Płoski, A note on the Łojasiewicz exponent at infinity, Bull. Soc. Sci. Lettres Łódź 44 (17) (1994), 11-15. Zbl0883.32022

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