2021/06/26 by Arturo Giles Flores, Flores, Arturo Giles, Otoniel Nogueira da Silva +3
Mathematics · #Meromorphic and Entire Functions #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2106.14106
From a procedure to calculate the C5-cone of a reduced complex analytic curve X ⊂ ℂn at a singular point 0 ∈ X, 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 C5-cone. We finish by giving an example showing that in a Lipschitz equisingular family of curves the number of planes in the C5-cone may not be constant.