Geodesic
On the fifth Whitney cone of a complex analytic curve
Journal of Singularities, Tome 24 (2022), pp. 96-118

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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. 
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     author = {A. Giles Flores and O. N. Silva and J. Snoussi},
     title = {On the fifth {Whitney} cone of a complex analytic curve},
     journal = {Journal of Singularities},
     pages = {96--118},
     publisher = {mathdoc},
     volume = {24},
     year = {2022},
     doi = {10.5427/jsing.2022.24c},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24c/}
}
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A. Giles Flores; O. N. Silva; J. Snoussi. On the fifth Whitney cone of a complex analytic curve. Journal of Singularities, Tome 24 (2022), pp. 96-118. doi: 10.5427/jsing.2022.24c

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