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

Janusz Gwoździewicz, and Arkadiusz Płoski. "Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables." Colloquium Mathematicae 103.1 (2005): 47-60. <http://eudml.org/doc/283647>.

@article{JanuszGwoździewicz2005,
abstract = {For every polynomial F in two complex variables we define the Łojasiewicz exponents $ℒ_\{p,t\}(F)$ measuring the growth of the gradient ∇F on the branches centered at points p at infinity such that F approaches t along γ. We calculate the exponents $ℒ_\{p,t\}(F)$ in terms of the local invariants of singularities of the pencil of projective curves associated with F.},
author = {Janusz Gwoździewicz, Arkadiusz Płoski},
journal = {Colloquium Mathematicae},
keywords = {Lojasiewicz exponent; equisingularity at infinity; polar curves},
language = {eng},
number = {1},
pages = {47-60},
title = {Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables},
url = {http://eudml.org/doc/283647},
volume = {103},
year = {2005},
}

TY - JOUR
AU - Janusz Gwoździewicz
AU - Arkadiusz Płoski
TI - Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables
JO - Colloquium Mathematicae
PY - 2005
VL - 103
IS - 1
SP - 47
EP - 60
AB - For every polynomial F in two complex variables we define the Łojasiewicz exponents $ℒ_{p,t}(F)$ measuring the growth of the gradient ∇F on the branches centered at points p at infinity such that F approaches t along γ. We calculate the exponents $ℒ_{p,t}(F)$ in terms of the local invariants of singularities of the pencil of projective curves associated with F.
LA - eng
KW - Lojasiewicz exponent; equisingularity at infinity; polar curves
UR - http://eudml.org/doc/283647
ER -