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Quotients jacobiens : une approche algébrique

  • Carine Reydy (a1)
Résumé

Le diagramme d’Eisenbud et Neumann d’un germe est un arbre qui représente ce germe et permet d’en calculer les invariants. On donne une démonstration algébrique d’un résultat caract érisant l’ensemble des quotients jacobiens d’un germe d’application (f, g) à partir du diagramme d’Eisenbud et Neumann de fg.

Abstract

The Eisenbud and Neumann diagram of a plane curve germis a tree that represents this germ and allows computation of its invariants. We algebraically show a result that gives a caracterization of the set of jacobian quotients of an application germ (f, g) for the datum of the Eisenbud et Neumann diagram of fg.

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References
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[A] Abhyankar, S S., Lectures on Expansion Techniques in Algebraic Geometry. Notes by Balwant Singh. Tata Institute of Fundamental Research Lectures on Mathematics and Physics 57, Tata Institute of Fundamental Research, Bombay, 1977.
[BK] Brieskorn, E. et Knörrer, H., Plane Algebraic Curves. Birkhäuser Verlag, Basel, 1986.
[CA] Casas-Alvero, E., Singularities of plane curves. London Mathematical Society Lecture Note Series 276. Cambridge University Press, Cambridge, 2000.
[EN] Eisenbud, D. et Neumann, W. D.. Three-dimensional link theory and invariants of plane curve singularities. Annals of Mathematics Studies 110, Princeton University Press, Princeton, NJ, 1985.
[GB] García Barroso, Evelia R., Courbes polaires et courbure des fibres de Milnor des courbes planes. Thèse de doctorat. Université Paris-7, 2000.
[H] Heitmann, R. C., On the Jacobian conjecture. J. Pure Appl. Algebra 64(1990), 3572.
[Hi] Hironaka, H., Introduction to the theory of infinitely near singular points. Memorias de Matematica del instituto Jorge Juan, 28, Consejo Superior de Investigaciones Cientficas, Madrid, 1974.
[KP] Kuo, T-C et Parusiński, A., On Puiseux roots of Jacobians. Proc. Japan Acad. Ser. A Math. Sci. 78(2002), no. 5, 5559.
[L] , D. T., Calcul du nombre de cycles évanouissants d’une hypersurface complexe. Ann. Inst. Fourier (Grenoble) 23(1973) no. 4, 261270.
[LMW] , D. T., Michel, F. et Weber, C., Sur le comportement des polaires associées aux germes de courbes planes. Compositio Math. 72(1989), no. 1, 87113.
[M] Maugendre, H., Topologie des germes jacobiens. C. R. Acad. Sci. Paris Sér. I, 322(1996), 945948.
[Me] Merle, M., Invariants polaires des courbes planes. Invent. Math. 41(1977), no. 2, 103111.
[R] Reydy, C., Étude d’invariants des germes de courbes planes à l’aide des diagrammes de Newton. Thèse de doctorat, Université Bordeaux I, 2002.
[T] Teissier, B., Variétés polaires. I. Invariants polaires des singularités d’hypersurfaces. Invent.Math. 40(1977), no. 3, 267292.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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