Abstract
In this paper we give an analogue of the dual graph for a space curve. Taking an embedded resolution, we consider the graph whose vertices are the components of the exceptional divisor, with edges joining intersecting components, and appropriate weights which determine the complete geometry of all infinitely near points associated with the curve.
Partially supported by D.G.I.C.Y.T. no PB 88-0344-C-03-01
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References
Campillo, A. & Castellanos, J.: “On projections of space curves”, in: “Algebraic Geometry”, Lecture Notes in Math. 961 (Springer, 1982), 22–31.
Casas, E.: Manuscript notes, 1989.
Castellanos, J.: “A relation between the multiplicity sequence and the semigroup of values of an algebroid curve”, Journal of Pure and Applied Algebra, vol. 43 (119–127) 1986.
Castellanos, J.: “Hamburger-Noether matrices over rings”, Journal of Pure and Applied Algebra, vol. 64, 1990.
Lipman, J.: “Stable ideals and Arfrings”, Amer. J. Math. 93 (1971) 649–685.
Van der Waerden, B.L.: “Infinitely near points”, Indiana Math. J. vol. 12 (1950) 401–410.
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© 1991 Springer-Verlag Berlin Heidelberg
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Castellanos, J. (1991). The dual graph for space curves. In: Mond, D., Montaldi, J. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086375
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DOI: https://doi.org/10.1007/BFb0086375
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