The Łojasiewicz numbers and plane curve singularities

Volume 87 / 2005

Evelia García Barroso, Tadeusz Krasiński, Arkadiusz Płoski Annales Polonici Mathematici 87 (2005), 127-150 MSC: 32S05, 14H20. DOI: 10.4064/ap87-0-11

Abstract

For every holomorphic function in two complex variables with an isolated critical point at the origin we consider the Łojasiewicz exponent $\mathcal{L}_{0}(f)$ defined to be the smallest $\theta>0$ such that $\vert {\rm grad} f(z)\vert \geq c \vert z\vert ^{\theta}$ near $0\in\mathbb{C}^{2}$ for some $c>0$. We investigate the set of all numbers $\mathcal{L}_{0}(f)$ where $f$ runs over all holomorphic functions with an isolated critical point at $0\in\mathbb{C}^{2}$.

Authors

  • Evelia García BarrosoDepartamento de
    Matemática Fundamental
    Facultad de Matemáticas
    Universidad de La Laguna
    38271 La Laguna, Tenerife, España
    e-mail
  • Tadeusz KrasińskiFaculty of Mathematics
    University of Łódź
    Banacha 22
    90-238 Łódź, Poland
    e-mail
  • Arkadiusz PłoskiDepartment of Mathematics
    Technical University
    Al. 1000 LPP 7
    25-314 Kielce, Poland
    e-mail

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