The Łojasiewicz numbers and plane curve singularities

Evelia García Barroso, Tadeusz Krasiński, and Arkadiusz Płoski. "The Łojasiewicz numbers and plane curve singularities." Annales Polonici Mathematici 87.1 (2005): 127-150. <http://eudml.org/doc/280347>.

@article{EveliaGarcíaBarroso2005,
abstract = {For every holomorphic function in two complex variables with an isolated critical point at the origin we consider the Łojasiewicz exponent ₀(f) defined to be the smallest θ > 0 such that $|grad f(z)| ≥ c|z|^\{θ\}$ near 0 ∈ ℂ² for some c > 0. We investigate the set of all numbers ₀(f) where f runs over all holomorphic functions with an isolated critical point at 0 ∈ ℂ².},
author = {Evelia García Barroso, Tadeusz Krasiński, Arkadiusz Płoski},
journal = {Annales Polonici Mathematici},
keywords = {Lojasiewicz exponent; plane curve singularity; characteristic sequence; intersection multiplicity},
language = {eng},
number = {1},
pages = {127-150},
title = {The Łojasiewicz numbers and plane curve singularities},
url = {http://eudml.org/doc/280347},
volume = {87},
year = {2005},
}

TY - JOUR
AU - Evelia García Barroso
AU - Tadeusz Krasiński
AU - Arkadiusz Płoski
TI - The Łojasiewicz numbers and plane curve singularities
JO - Annales Polonici Mathematici
PY - 2005
VL - 87
IS - 1
SP - 127
EP - 150
AB - For every holomorphic function in two complex variables with an isolated critical point at the origin we consider the Łojasiewicz exponent ₀(f) defined to be the smallest θ > 0 such that $|grad f(z)| ≥ c|z|^{θ}$ near 0 ∈ ℂ² for some c > 0. We investigate the set of all numbers ₀(f) where f runs over all holomorphic functions with an isolated critical point at 0 ∈ ℂ².
LA - eng
KW - Lojasiewicz exponent; plane curve singularity; characteristic sequence; intersection multiplicity
UR - http://eudml.org/doc/280347
ER -