The polar curve of a foliation on ${\mathbb{P}}^2$

Mol, Rogério S.. "The polar curve of a foliation on $\mathbb{P}^2$." Annales de la faculté des sciences de Toulouse Mathématiques 19.3-4 (2010): 849-863. <http://eudml.org/doc/115886>.

@article{Mol2010,
abstract = {We study some properties of the polar curve $\{\hbox\{$P$\}\}^\{\{\mathcal\{F\}\}\}_\{l\}$ associated to a singular holomorphic foliation $\{\mathcal\{F\}\}$ on the complex projective plane $\{\mathbb\{P\}\}^\{2\}$. We prove that, for a generic center $l \in \{\mathbb\{P\}\}^\{2\}$, the curve $\{\hbox\{$P$\}\}^\{\{\mathcal\{F\}\}\}_\{l\}$ is irreducible and its singular points are exactly the singular points of $\{\mathcal\{F\}\}$ with vanishing linear part. We also obtain upper bounds for the algebraic multiplicities of the singularities of $\{\mathcal\{F\}\}$ and for its number of radial singularities.},
affiliation = {Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627 C.P. 702, 30123-970 - Belo Horizonte - MG, BRAZIL},
author = {Mol, Rogério S.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {polar curve; singular holomorphic foliation; radial singularities},
language = {eng},
number = {3-4},
pages = {849-863},
publisher = {Université Paul Sabatier, Toulouse},
title = {The polar curve of a foliation on $\mathbb\{P\}^2$},
url = {http://eudml.org/doc/115886},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Mol, Rogério S.
TI - The polar curve of a foliation on $\mathbb{P}^2$
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2010
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - 3-4
SP - 849
EP - 863
AB - We study some properties of the polar curve ${\hbox{$P$}}^{{\mathcal{F}}}_{l}$ associated to a singular holomorphic foliation ${\mathcal{F}}$ on the complex projective plane ${\mathbb{P}}^{2}$. We prove that, for a generic center $l \in {\mathbb{P}}^{2}$, the curve ${\hbox{$P$}}^{{\mathcal{F}}}_{l}$ is irreducible and its singular points are exactly the singular points of ${\mathcal{F}}$ with vanishing linear part. We also obtain upper bounds for the algebraic multiplicities of the singularities of ${\mathcal{F}}$ and for its number of radial singularities.
LA - eng
KW - polar curve; singular holomorphic foliation; radial singularities
UR - http://eudml.org/doc/115886
ER -