The dimension of the Chow variety of curves
David Eisenbud, Joe Harris (1992)
Compositio Mathematica
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David Eisenbud, Joe Harris (1992)
Compositio Mathematica
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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 or 1 node in meeting an appropriate generic collection of points and lines. As a byproduct, we also compute the number of rational plane curves of degree passing through given points and tangent to a given line. The method is ‘classical’, free of Quantum Cohomology.
Stefan Kebekus, Sándor J. Kovács (2004)
Annales de l’institut Fourier
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Let 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 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.
Sheldon Katz (1986)
Compositio Mathematica
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Robert Lazarsfeld (1981)
Compositio Mathematica
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Tom Graber, Joe Harris, Barry Mazur, Jason Starr (2005)
Annales scientifiques de l'École Normale Supérieure
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