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Osculating degeneration of curves

Mallavibarrena Martínez de Castro, Raquel and González Pascual, Sonia (2003) Osculating degeneration of curves. Communications in Algebra, 31 (8). pp. 3829-3845. ISSN 0092-7872

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Abstract

The main objects of this paper are osculating spaces of order m to smooth algebraic curves, with the property of meeting the curve again. We prove that the only irreducible curves with an infinite number of this type of osculating spaces of order m are curves in Pm+1 Whose degree n is greater than m + 1. This is a generalization of the result and proof of Kaji (Kaji, H. (1986). On the tangentially degenerate curves. J. London Math. Soc. 33(2)-430-440) that corresponds to the case m = 1. We also obtain an enumerative formula for the number of those osculating spaces to curves in Pm+2. The case m = 1 of it is a classical formula proved with modern techniques. by Le Barz (Le Barz, P. (1982). Formules multisecantes pour les courbes gauches quelconques. In: Enumerative Geometry and Classical Algebraic Geometry. Prog. in Mathematics 24, Birkhauser, pp. 165-197).


Item Type:Article
Uncontrolled Keywords:osculating space; Hilbert scheme of points; curve; enumerative formula
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:16624
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Deposited On:04 Oct 2012 08:37
Last Modified:07 Feb 2014 09:32

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