Are rational curves determined by tangent vectors?
Annales de l'Institut Fourier, Volume 54 (2004) no. 1, p. 53-79
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.
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
DOI : https://doi.org/10.5802/aif.2010
Classification:  14M99,  14J45,  14J99
Keywords: Fano manifold, rational curve of minimal degree
@article{AIF_2004__54_1_53_0,
     author = {Kebekus, Stefan and Kov\'acs, S\'andor J.},
     title = {Are rational curves determined by tangent vectors?},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {1},
     year = {2004},
     pages = {53-79},
     doi = {10.5802/aif.2010},
     zbl = {1067.14023},
     mrnumber = {2069121},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_1_53_0}
}
Kebekus, Stefan; Kovács, Sándor J. Are rational curves determined by tangent vectors?. Annales de l'Institut Fourier, Volume 54 (2004) no. 1, pp. 53-79. doi : 10.5802/aif.2010. http://www.numdam.org/item/AIF_2004__54_1_53_0/

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