On the fifth Whitney cone of a complex analytic curve
Arturo Giles Flores, Otoniel Nogueira da Silva, Jawad Snoussi

TL;DR
This paper introduces auxiliary multiplicities derived from the fifth Whitney cone of complex analytic curves, which characterize Lipschitz singularity types and refine bounds on the cone's components.
Contribution
It defines auxiliary multiplicities for the $C_5$-cone, linking them to Lipschitz classification and improving bounds on the number of cone components.
Findings
Auxiliary multiplicities characterize Lipschitz types of curve singularities.
Bounds for the number of $C_5$-cone components are improved.
The number of planes in the $C_5$-cone can vary in Lipschitz equisingular families.
Abstract
From a procedure to calculate the -cone of a reduced complex analytic curve at a singular point , we extract a collection of integers that we call {\it 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 -cone. We finish by giving an example showing that in a Lipschitz equisingular family of curves the number of planes in the -cone may not be constant.
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Taxonomy
TopicsMeromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory
