Zariski Invariant For Non-Isolated Separatrices Through Jacobian Curves of Pseudo-Cuspidal Dicritical Foliations
Oziel Gómez-Martínez
Journal of Singularities
volume 23 (2021), 236-270
Received: 12 March 2021. Received in revised form: 6 November 2021.
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Abstract:
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.
2010 Mathematical Subject Classification:
Key words and phrases:
Dicritical foliations, non-isolated separatrices, analytic invariants of plane branches, polar curves
Author(s) information:
Oziel Gómez-Martínez
Instituto de Matemàticas
Universidad Nacional Autónoma de México (UNAM)
Área de la Investigación Científica, Circuito exterior
Ciudad Universitaria
04510, Ciudad de México, México.
email: ogomez@im.unam.mx
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