Multiplicity and Semicontinuity of the Łojasiewicz Exponent

Volume 64 / 2016

Tomasz Rodak, Adam Różycki, Stanisław Spodzieja Bulletin Polish Acad. Sci. Math. 64 (2016), 55-62 MSC: 32B10, 14Q99, 12Y99. DOI: 10.4064/ba8041-3-2016 Published online: 18 March 2016

Abstract

We give an effective formula for the improper isolated multiplicity of a polynomial mapping. Using this formula we construct, for a given deformation of a holomorphic mapping with an isolated zero at zero, a stratification of the space of parameters such that the Łojasiewicz exponent is constant on each stratum.

Authors

  • Tomasz RodakFaculty of Mathematics and Computer Science
    University of Łódź
    S. Banacha 22
    90-238 Łódź, Poland
    e-mail
  • Adam RóżyckiFaculty of Mathematics and Computer Science
    University of Łódź
    S. Banacha 22
    90-238 Łódź, Poland
    e-mail
  • Stanisław SpodziejaFaculty of Mathematics and Computer Science
    University of Łódź
    S. Banacha 22
    90-238 Łódź, Poland
    e-mail

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