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An upper bound of the singularity order for the generic projection. (English) Zbl 0673.14018
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” \(t\to (t^ e,t^{e+1},...,t^{2e-1})\).
Reviewer: A.Buium

MSC:
14H20 Singularities of curves, local rings
14E05 Rational and birational maps
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
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References:
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[2] Serre, J.-P., Groupes algébriques et corps de classes, () · Zbl 0097.35604
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