Geodesic
Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables
Janusz Gwoździewicz 1   ; Arkadiusz Płoski 2
1 Technical University Aleja 1000LPP 7 25-314 Kielce, Poland
2 Technical University Aleja 1000LPP 7 25–314 Kielce, Poland
Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 47-60 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $F$.
DOI : 10.4064/cm103-1-7
Keywords: every polynomial complex variables define ojasiewicz exponents measuring growth gradient nabla branches centered points infinity approaches along gamma calculate exponents terms local invariants singularities pencil projective curves associated

Janusz Gwoździewicz  1   ; Arkadiusz Płoski  2

1 Technical University Aleja 1000LPP 7 25-314 Kielce, Poland
2 Technical University Aleja 1000LPP 7 25–314 Kielce, Poland 
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 at infinity of polynomials in two complex variables
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Janusz Gwoździewicz; Arkadiusz Płoski. Łojasiewicz exponents and singularities
 at infinity of polynomials in two complex variables. Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 47-60. doi: 10.4064/cm103-1-7

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