Resumo: In this talk we will describe a procedure to determine the cone $C_5$ associated to a complex curve singularity. This procedure comes out with a collection of integers that we call auxiliary multiplicity. We prove that these multiplicities determine the bi-Lipschitz type of the curve singularity. We also give bounds on the number of irreducible components of the $C_5$-cone of a curve singularity. This is a joint work with Arturo Giles Flores and Otoniel Nogueira da Silva.






