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ArticleOriginal scientific text

Title

Resultant and the Łojasiewicz exponent

Authors 1, 1

Affiliations

  1. Institute of Mathematics, University of Łódź, S. Banacha 22, 90-238 Łódź, Poland

Abstract

An effective formula for the Łojasiewicz exponent of a polynomial mapping of ℂ² into ℂ² at an isolated zero in terms of the resultant of its components is given.

Keywords

ENG
holomorphic mapping, polynomial mapping, Łojasiewicz exponent, resultant

Bibliography

  1. [C] J. Chądzyński, On the order of an isolated zero of a holomorphic mapping, Bull. Polish Acad. Sci. Math. 31 (1983), 121-128.
  2. [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.
  3. [CK₂] J. Chądzyński and T. Krasiński, On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ² , Ann. Polon. Math. 57 (1992), 291-302.
  4. [CP] J. Chądzyński and A. Płoski, An inequality for the intersection multiplicity of analytic curves, Bull. Polish Acad. Sci. Math. 36 (1988), 113-117.
  5. [LT] M. Lejeune-Jalabert et B. Teissier, Clôture intégrale des idéaux et équisingularité, Centre de Mathématiques, École Polytechnique, 1974.
  6. [P] A. Płoski, Multiplicity and the Łojasiewicz exponent, in: Singularities, S. Łojasiewicz (ed.), Banach Center Publ. 20, PWN, Warszawa, 1988, 353-364.
  7. [W] R. J. Walker, Algebraic Curves, Springer, New York, 1978.
Annales Polonici Mathematici
1995/61/1
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Pages:
95-100
Main language of publication
English
Received
1994-05-18
Published
1995
Exact and natural sciences