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

Janusz Gwoździewicz; Arkadiusz Płoski

Colloquium Mathematicae (2005)

- Volume: 103, Issue: 1, page 47-60
- ISSN: 0010-1354

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topJanusz 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 -

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