Are rational curves determined by tangent vectors?
[Les courbes rationnelles de degré minimal sont-elles déterminées par leurs vecteurs tangents ?]
Kebekus, Stefan1 ; Kovács, Sándor J.2
1 Universität zu Köln, Mathematisches Institut, Weyertal 86--90, 50931 Köln (Allemagne)
2 University of Washington, Department of mathematics, Box 354350, Seattle, WA 98195 (USA)
Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 53-79.

Soit X une variété projective, revêtue par des courbes rationnelles, par exemple une variété de Fano sur le corps des nombres complexes. Dans cet article, nous donnons des conditions suffisantes pour que tout vecteur tangent en un point général de X soit tangent à au plus une courbe rationnelle de degré minimal. Comme conséquence immédiate, nous obtenons un critère d’irréductibilité de l’espace des courbes rationnelles de degré minimal

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.

DOI : 10.5802/aif.2010
Classification : 14M99, 14J45, 14J99
Keywords: Fano manifold, rational curve of minimal degree
Mot clés : variété de Fano, courbe rationnelle de degré minimal
Kebekus, Stefan 1 ; Kovács, Sándor J. 2

1 Universität zu Köln, Mathematisches Institut, Weyertal 86--90, 50931 Köln (Allemagne)
2 University of Washington, Department of mathematics, Box 354350, Seattle, WA 98195 (USA) 
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Kebekus, Stefan; Kovács, Sándor J. Are rational curves determined by tangent vectors?. Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 53-79. doi : 10.5802/aif.2010. http://www.numdam.org/articles/10.5802/aif.2010/

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