Acta Mathematica Vietnamica

We introduce, using resolution of singularities, a new invariant $\lambda (f)$ of a plane curve singularity $f$ which can be easily computed and study its relation to the problem of the stability under small perturbations. More percisely, we prove that the number of braches and delta invatiants of plane curve singularities are stable under small perturbations of degree at least $\lambda (f)$.

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