Geodesic
Zariski Invariant For Non-Isolated Separatrices Through Jacobian Curves of Pseudo-Cuspidal Dicritical Foliations
Journal of Singularities, Tome 23 (2021), pp. 236-270

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In this work, we consider a sequence π of blowing-up morphisms in (C^2, 0) corresponding to the reduction of singularities of an (n,m)-cuspidal branch and we consider as well the family of pseudo-cuspidal dicritical foliations, which consists of those dicritical foliations that have exactly one dicritical component in the last divisor of π. This family contains the family of (n,m)-cuspidal dicritical foliations that are given by a vector field with non-degenerate linear part. We prove that the Zariski invariant of every pair of non-isolated separatrices of any pseudo-cuspidal dicritical foliation that has polar transversality with the (n,m)-cuspidal dicritical foliations that are given by a vector field with non-degenerate linear part, coincides.
DOI : 10.5427/jsing.2021.23m
Classification : 
@article{10_5427_jsing_2021_23m,
     author = {Oziel G\'omez-Mart{\'\i}nez},
     title = {Zariski {Invariant} {For} {Non-Isolated} {Separatrices} {Through} {Jacobian} {Curves} of {Pseudo-Cuspidal} {Dicritical} {Foliations}},
     journal = {Journal of Singularities},
     pages = {236--270},
     publisher = {mathdoc},
     volume = {23},
     year = {2021},
     doi = {10.5427/jsing.2021.23m},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2021.23m/}
}
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TI  - Zariski Invariant For Non-Isolated Separatrices Through Jacobian Curves of Pseudo-Cuspidal Dicritical Foliations
JO  - Journal of Singularities
PY  - 2021
SP  - 236
EP  - 270
VL  - 23
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DO  - 10.5427/jsing.2021.23m
ID  - 10_5427_jsing_2021_23m
ER  - 
%0 Journal Article
%A Oziel Gómez-Martínez
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%J Journal of Singularities
%D 2021
%P 236-270
%V 23
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2021.23m/
%R 10.5427/jsing.2021.23m
%F 10_5427_jsing_2021_23m
Oziel Gómez-Martínez. Zariski Invariant For Non-Isolated Separatrices Through Jacobian Curves of Pseudo-Cuspidal Dicritical Foliations. Journal of Singularities, Tome 23 (2021), pp. 236-270. doi: 10.5427/jsing.2021.23m

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