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Stefan Kebekus; Sándor J. Kovács
Are rational curves determined by tangent vectors?
(Les courbes rationnelles de degré minimal sont-elles déterminées par leurs vecteurs tangents ?)
Annales de l'institut Fourier, 54 no. 1 (2004), p. 53-79, doi: 10.5802/aif.2010
Article PDF | Reviews MR 2069121 | Zbl 1067.14023
Class. Math.: 14M99, 14J45, 14J99
Keywords: Fano manifold, rational curve of minimal degree

Résumé - Abstract

Let $X$ be a projective variety which is covered by rational curves, for instance a Fano manifold over the complex numbers. In this paper, we give sufficient conditions which guarantee that every tangent vector at a general point of $X$ is contained in at most one rational curve of minimal degree. As an immediate application, we obtain irreducibility criteria for the space of minimal rational curves.

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