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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[D] [D] Davis, E. D., On the geometric interpretation of seminormality, Proc. of A.M.S., Vol. 68, (1978), 1-5. Google Scholar

[F] [F] Fulton, W., Algebraic curves, Mathematics Lecture Note Series, W. A. Benjamin, New York (1969). Google Scholar

[H] [H] Hartshorne, R., Algebraic geometry, Graduate texts in mathematics, Springer Verlag, New York, (1977). Google Scholar

[L] [L] Lipman, J., Stable ideals and Arf rings, Amer. J. Math., Vol. 93, (1971), 649-685. Google Scholar

[M] [M] Mumford, D., Introduction to algebraic geometry, Harvard Lecture Notes, (1967). Google Scholar

[O] [O] Orecchia, F., Points in generic position and conductor of curves with ordinary singularities, Queen's Mathematical Preprint, No. 1979-26. Google Scholar

[S] [S] Sally, J., Number of generators of ideals in local rings, Lect. Notes in Pure and Applied Math., Marcel Dekker, New York, (1978). Google Scholar

[Sh] [Sh] Shafarevich, I. R., Basic algebraic geometry, Grundlehren 213, Springer Verlag, Heildelberg (1974). Google Scholar

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