An upper bound of the singularity order for the generic projection (Q1120631)

Let X be an algebroid curve of multiplicity e in \((k^ N,0)\), \(\tilde X\) be Zariski's absolute saturation of X and \(X'\) a generic plane projection of X. The author proves that \(\delta (X')\) is not bigger than \((e-1)\delta(\tilde X)-(e-1)(e-2)/2,\) where \(\delta\) denotes as usual the codimension of the local ring of the singularity in its normalisation. Moreover the author proves that equality holds iff X is isomorphic to the ``monomial curve'' \(t\to (t^ e,t^{e+1},...,t^{2e-1})\).