Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables
Volume 103 / 2005
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 $F$.
