Displaying similar documents to “Counting rational curves of arbitrary shape in projective spaces.”

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.

Smoothing of rational m-ropes

Edoardo Ballico, Elizabeth Gasparim, Thomas Köppe (2009)

Open Mathematics

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In a recent paper, Gallego, González and Purnaprajna showed that rational 3-ropes can be smoothed. We generalise their proof, and obtain smoothability of rational m-ropes for m ≥ 3.