On the fifth Whitney cone of a complex analytic curve

A. Giles Flores, O. N. Silva, J. Snoussi

Journal of Singularities
volume 24 (2022), 96-118

Received: 25 August 2021. Received in revised form: 23 May 2022.

DOI: 10.5427/jsing.2022.24c

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Abstract:

From a procedure to calculate the C_5-cone of a reduced complex analytic curve X contained in C^n at a singular point 0 in X, we extract a collection of integers that we call auxiliary multiplicities and we prove they characterize the Lipschitz type of complex curve singularities. We then use them to improve the known bounds for the number of irreducible components of the C_5-cone. We finish by giving an example showing that in a Lipschitz equisingular family of curves the number of planes in the C_5-cone may not be constant.

Author(s) information:

Arturo Giles Flores
Departamento de Matemáticas y Física
Universidad Autónoma de Aguascalientes
Aguascalientes, México
email: arturo.giles@cimat.mx

Otoniel Nogueira Silva
Departamento de Matemática
Universidade Federal da Paraíba
João Pessoa, Brazil
email: otoniel.silva@academico.ufpb.br

Jawad Snoussi
Instituto de Matemáticas
Universidad Nacional Autónoma de México (UNAM)
Unidad Cuernavaca, México
email: jsnoussi@im.unam.mx