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Displaying similar documents to “Generalized Mukai conjecture for special Fano varieties”

Enumerative geometry of divisorial families of rational curves

Ziv Ran (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We compute the number of irreducible rational curves of given degree with 1 tacnode in 2 or 1 node in 3 meeting an appropriate generic collection of points and lines. As a byproduct, we also compute the number of rational plane curves of degree d passing through 3 d - 2 given points and tangent to a given line. The method is ‘classical’, free of Quantum Cohomology.

Are rational curves determined by tangent vectors?

Stefan Kebekus, Sándor J. Kovács (2004)

Annales de l’institut Fourier

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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.