Geodesic
Ordinary Singularities of Algebraic Curves
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 423-431

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Let A be the local ring at a singular point p of an algebraic reduced curve. Let M (resp. Ml,..., Mh ) be the maximal ideal of A (resp. of Ā). In this paper we want to classify ordinary singularities p with reduced tangent cone: Spec(G(A)). We prove that G(A) is reduced if and only if: p is an ordinary singularity, and the vector spaces span the vector space . If the points of the projectivized tangent cone Proj(G(A)) are in generic position then p is an ordinary singularity if and only if G(A) is reduced. We give an example which shows that the preceding equivalence is not true in general.
DOI : 10.4153/CMB-1981-065-6
Mots-clés : 13H15, 14H20, 14H45, Algebraic curve, ordinary singularity, branches, tangent cone, tangent space, Veronese embedding 
Orecchia, Ferruccio. Ordinary Singularities of Algebraic Curves. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 423-431. doi: 10.4153/CMB-1981-065-6
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     title = {Ordinary {Singularities} of {Algebraic} {Curves}},
     journal = {Canadian mathematical bulletin},
     pages = {423--431},
     year = {1981},
     volume = {24},
     number = {4},
     doi = {10.4153/CMB-1981-065-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-065-6/}
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