On the Variety of Smooth Rational Space Curves with Given Degree and Normal Bundle.
David Eisenbud, A. Van de Ven (1982)
Inventiones mathematicae
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David Eisenbud, A. Van de Ven (1982)
Inventiones mathematicae
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Franco Ghione, Gianni Sacchiero (1980/81)
Manuscripta mathematica
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Bjorn Poonen (2009)
Journal of the European Mathematical Society
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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.
Matei Toma (1996)
Manuscripta mathematica
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Masahiro Yasumoto (1994)
Manuscripta 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.
K. Hulek, A. de Van de Ven (1985)
Manuscripta mathematica
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Herbert Lange (1984)
Manuscripta mathematica
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Pittie, Harsh, Ram, Arun (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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M. Andreatta, M. Palleschi (1991)
Manuscripta mathematica
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Yoshifumi Takeda (2007)
Colloquium Mathematicae
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The pre-Tango structure is an ample invertible sheaf of locally exact differentials on a variety of positive characteristic. It is well known that pre-Tango structures on curves often induce pathological uniruled surfaces. We show that almost all pre-Tango structures on varieties induce higher-dimensional pathological uniruled varieties, and that each of these uniruled varieties also has a pre-Tango structure. For this purpose, we first consider the p-closed rational vector field...