Mallavibarrena Martínez de Castro, Raquel2023-06-212023-06-211986-11-210764-4442https://hdl.handle.net/20.500.14352/64678In 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.frajournal articlehttp://gallica.bnf.fr/ark:/12148/bpt6k5496856f/f41.image.r=COMPTES%20RENDUS%20DE%20L%20ACADEMIE%20DES%20SCIENCES%20SERIE%20I-MATHEMATIQUE.langEShttp://gallica.bnf.fr/ark:/restricted access512.7stationary trisecantChow groups of Hilbert schemesGeometria algebraica1201.01 Geometría Algebraica