Łojasiewicz exponents and singularities
at infinity of polynomials in two complex variables
Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 47-60
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $F$.
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
Affiliations des auteurs :
Janusz Gwoździewicz 1 ; Arkadiusz Płoski 2
@article{10_4064_cm103_1_7,
author = {Janusz Gwo\'zdziewicz and Arkadiusz P{\l}oski},
title = {{\L}ojasiewicz exponents and singularities
at infinity of polynomials in two complex variables},
journal = {Colloquium Mathematicum},
pages = {47--60},
publisher = {mathdoc},
volume = {103},
number = {1},
year = {2005},
doi = {10.4064/cm103-1-7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm103-1-7/}
}
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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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