The polar curve of a foliation on 2
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 3-4, p. 849-863
On étudie dans cet article quelques propriétés de la courbe polaire P l associée à un feuilletage holomorphe singulier dans le plan projectif complexe 2 . On démontre que, pour un centre l 2 générique, la courbe P l est irréductible et ses points singuliers sont précisément les points singuliers de avec partie linéaire nulle. On obtient aussi des bornes supérieurs pour la multiplicité algébrique des singularités de et pour son nombre de singularités radiales.
We study some properties of the polar curve P l associated to a singular holomorphic foliation on the complex projective plane 2 . We prove that, for a generic center l 2 , the curve P l is irreducible and its singular points are exactly the singular points of with vanishing linear part. We also obtain upper bounds for the algebraic multiplicities of the singularities of and for its number of radial singularities.
@article{AFST_2010_6_19_3-4_849_0,
     author = {Mol, Rog\'erio S.},
     title = {The polar curve of a foliation on $\mathbb{P}^2$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 19},
     number = {3-4},
     year = {2010},
     pages = {849-863},
     doi = {10.5802/afst.1268},
     mrnumber = {2790820},
     zbl = {1254.53050},
     language = {en},
     url = {http://http://www.numdam.org/item/AFST_2010_6_19_3-4_849_0}
}
Mol, Rogério S. The polar curve of a foliation on $\mathbb{P}^2$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 3-4, pp. 849-863. doi : 10.5802/afst.1268. http://www.numdam.org/item/AFST_2010_6_19_3-4_849_0/

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