For every polynomial F in two complex variables we define the Łojasiewicz exponents 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 in terms of the local invariants of singularities of the pencil of projective curves associated with F.
@article{bwmeta1.element.bwnjournal-article-doi-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 Mathematicae},
volume = {103},
year = {2005},
pages = {47-60},
zbl = {1095.32012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-7}
}
Janusz Gwoździewicz; Arkadiusz Płoski. Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables. Colloquium Mathematicae, Tome 103 (2005) pp. 47-60. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-7/