On the Łojasiewicz exponent of the gradient of a polynomial function

Andrzej Lenarcik. "On the Łojasiewicz exponent of the gradient of a polynomial function." Annales Polonici Mathematici 71.3 (1999): 211-239. <http://eudml.org/doc/262851>.

@article{AndrzejLenarcik1999,
abstract = {Let $h = ∑ h_\{αβ\} X^αY^β$ be a polynomial with complex coefficients. The Łojasiewicz exponent of the gradient of h at infinity is the least upper bound of the set of all real λ such that $|grad h(x,y)| ≥ c|(x,y)|^λ$ in a neighbourhood of infinity in ℂ², for c > 0. We estimate this quantity in terms of the Newton diagram of h. Equality is obtained in the nondegenerate case.},
author = {Andrzej Lenarcik},
journal = {Annales Polonici Mathematici},
keywords = {polynomial mapping; Łojasiewicz exponent; Newton diagram; Newton polygon},
language = {eng},
number = {3},
pages = {211-239},
title = {On the Łojasiewicz exponent of the gradient of a polynomial function},
url = {http://eudml.org/doc/262851},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Andrzej Lenarcik
TI - On the Łojasiewicz exponent of the gradient of a polynomial function
JO - Annales Polonici Mathematici
PY - 1999
VL - 71
IS - 3
SP - 211
EP - 239
AB - Let $h = ∑ h_{αβ} X^αY^β$ be a polynomial with complex coefficients. The Łojasiewicz exponent of the gradient of h at infinity is the least upper bound of the set of all real λ such that $|grad h(x,y)| ≥ c|(x,y)|^λ$ in a neighbourhood of infinity in ℂ², for c > 0. We estimate this quantity in terms of the Newton diagram of h. Equality is obtained in the nondegenerate case.
LA - eng
KW - polynomial mapping; Łojasiewicz exponent; Newton diagram; Newton polygon
UR - http://eudml.org/doc/262851
ER -