A+ CATEGORY SCIENTIFIC UNIT

Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables

Volume 103 / 2005

Janusz Gwoździewicz, Arkadiusz Płoski Colloquium Mathematicum 103 (2005), 47-60 MSC: 32S99, 14R99. DOI: 10.4064/cm103-1-7

Abstract

For every polynomial $F$ in two complex variables we define the Łojasiewicz exponents ${\it\$}_{p,t}(F)$ measuring the growth of the gradient $\nabla F$ on the branches centered at points $p$ at infinity such that $F$ approaches $t$ along $\gamma$. We calculate the exponents ${\it\$}_{p,t}(F)$ in terms of the local invariants of singularities of the pencil of projective curves associated with $F$.

Authors

  • Janusz GwoździewiczTechnical University
    Aleja 1000LPP 7
    25-314 Kielce, Poland
    e-mail
  • Arkadiusz PłoskiTechnical University
    Aleja 1000LPP 7
    25–314 Kielce, Poland
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image