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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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Official URL: http://www.tandfonline.com/doi/pdf/10.1081/AGB-120022445

## 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 |
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Uncontrolled Keywords: | osculating space; Hilbert scheme of points; curve; enumerative formula |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 16624 |

Deposited On: | 04 Oct 2012 08:37 |

Last Modified: | 25 Jul 2018 10:36 |

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