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Validité de la formule classique des trisécantes stationnaires



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Mallavibarrena Martínez de Castro, Raquel (1986) Validité de la formule classique des trisécantes stationnaires. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique , 303 (16). pp. 799-802. ISSN 0764-4442

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In projective 3-space over the complex numbers, a stationary trisecant of a non-singular curve C is a line meeting C in three points such that two of the tangents at these three points intersect. There are four classical formulas for space curves [see, for example {\it J. G. Semple} and {\it L. Roth}, "Introduction to algebraic geometry" (Oxford 1949); pp. 373- 377]. Classically, there was always the restriction of the generic case. {\it P. Le Barz} [C. R. Acad. Sci., Paris, Sér. A 289, 755-758 (1979; Zbl 0445.14025)] proved three of the formulas without this restriction. In this article, the fourth formula is also proved. The number of stationary tangents is $\xi =-5n\sp 3+27n\sp 2-34n+2h(n\sp 2+4n-22-2h)$ where n is the degree and h is the number of apparent double points. The complicated computation uses similar methods to those of Le Barz (loc. cit.) involving the Chow groups of Hilbert schemes.

Tipo de documento:Artículo
Palabras clave:stationary trisecant; Chow groups of Hilbert schemes
Materias:Ciencias > Matemáticas > Geometria algebraica
Código ID:16642
Depositado:08 Oct 2012 07:51
Última Modificación:08 May 2013 17:03

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