Elias, Juan An upper bound of the singularity order for the generic projection. (English) Zbl 0673.14018 J. Pure Appl. Algebra 53, No. 3, 267-270 (1988). 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 Cited in 1 Document MSC: 14H20 Singularities of curves, local rings 14E05 Rational and birational maps 14E15 Global theory and resolution of singularities (algebro-geometric aspects) Keywords:algebroid curve; saturation; generic plane projection; monomial curve PDF BibTeX XML Cite \textit{J. Elias}, J. Pure Appl. Algebra 53, No. 3, 267--270 (1988; Zbl 0673.14018) Full Text: DOI References: [1] Campillo, A., Algebroid curves in positive characteristic, () · Zbl 0451.14010 [2] Serre, J.-P., Groupes algébriques et corps de classes, () · Zbl 0097.35604 [3] Zariski, O.; Zariski, O.; Zariski, O., General theory of saturations and saturated local rings, Amer. J. math., Amer. J. math., Amer. J. math., 97, 3, 415-502, (1975) · Zbl 0306.13009 [4] Zariski, O., Studies in equisingularity, Amer. J. math., 90, 3, 961-1023, (1968) · Zbl 0189.21405 [5] Zariski, O., Le problème des modules pour LES branches planes, (1973), Cours donné au Centre de Math. de L’Ecole Polytechnique Paris This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.