# Are rational curves determined by tangent vectors?

Stefan Kebekus^{[1]}; Sándor J. Kovács^{[2]}

- [1] Universität zu Köln, Mathematisches Institut, Weyertal 86--90, 50931 Köln (Allemagne)
- [2] University of Washington, Department of mathematics, Box 354350, Seattle, WA 98195 (USA)

Annales de l’institut Fourier (2004)

- Volume: 54, Issue: 1, page 53-79
- ISSN: 0373-0956

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topKebekus, Stefan, and Kovács, Sándor J.. "Are rational curves determined by tangent vectors?." Annales de l’institut Fourier 54.1 (2004): 53-79. <http://eudml.org/doc/116108>.

@article{Kebekus2004,

abstract = {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.},

affiliation = {Universität zu Köln, Mathematisches Institut, Weyertal 86--90, 50931 Köln (Allemagne); University of Washington, Department of mathematics, Box 354350, Seattle, WA 98195 (USA)},

author = {Kebekus, Stefan, Kovács, Sándor J.},

journal = {Annales de l’institut Fourier},

keywords = {Fano manifold; rational curve of minimal degree; dubbies},

language = {eng},

number = {1},

pages = {53-79},

publisher = {Association des Annales de l'Institut Fourier},

title = {Are rational curves determined by tangent vectors?},

url = {http://eudml.org/doc/116108},

volume = {54},

year = {2004},

}

TY - JOUR

AU - Kebekus, Stefan

AU - Kovács, Sándor J.

TI - Are rational curves determined by tangent vectors?

JO - Annales de l’institut Fourier

PY - 2004

PB - Association des Annales de l'Institut Fourier

VL - 54

IS - 1

SP - 53

EP - 79

AB - 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.

LA - eng

KW - Fano manifold; rational curve of minimal degree; dubbies

UR - http://eudml.org/doc/116108

ER -

## References

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