Courbes rationnelles et droites en position générale

Robin Hartshorne; André Hirschowitz

Annales de l'institut Fourier (1985)

  • Volume: 35, Issue: 4, page 39-58
  • ISSN: 0373-0956

Abstract

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The general union of a rational curve and lines in P 3 is proven to be of maximal rank.

How to cite

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Hartshorne, Robin, and Hirschowitz, André. "Courbes rationnelles et droites en position générale." Annales de l'institut Fourier 35.4 (1985): 39-58. <http://eudml.org/doc/74697>.

@article{Hartshorne1985,
abstract = {On montre que la réunion générale d’une courbe rationnelle avec des droites dans $\{\bf P\}^3$ est de rang maximum.},
author = {Hartshorne, Robin, Hirschowitz, André},
journal = {Annales de l'institut Fourier},
keywords = {union of a rational curve and lines in projective 3-space; maximal rank},
language = {fre},
number = {4},
pages = {39-58},
publisher = {Association des Annales de l'Institut Fourier},
title = {Courbes rationnelles et droites en position générale},
url = {http://eudml.org/doc/74697},
volume = {35},
year = {1985},
}

TY - JOUR
AU - Hartshorne, Robin
AU - Hirschowitz, André
TI - Courbes rationnelles et droites en position générale
JO - Annales de l'institut Fourier
PY - 1985
PB - Association des Annales de l'Institut Fourier
VL - 35
IS - 4
SP - 39
EP - 58
AB - On montre que la réunion générale d’une courbe rationnelle avec des droites dans ${\bf P}^3$ est de rang maximum.
LA - fre
KW - union of a rational curve and lines in projective 3-space; maximal rank
UR - http://eudml.org/doc/74697
ER -

References

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  1. [1] E. BALLICO, Ph. ELLIA, Generic curves of small genus have maximal rank, Math. Ann., 264 (1983), 211-225. Zbl0501.14017
  2. [2] E. BALLICO, Ph. ELLIA, Sur la postulation des courbes de Pn et de leurs projections, C.R.A.S., 299 (1984), 237-240. Zbl0565.14012
  3. [3] E. BALLICO, Ph. ELLIA, The maximal rank conjecture for non special curves in P3, Invent. Math., 79 (1985), 541-555. Zbl0556.14007
  4. [4] D. EISENBUD, J. HARRIS, Divisors on general curves and cuspidal rational space curves, Invent. Math., (1983), 371-418. Zbl0527.14022MR85h:14019
  5. [5] D. EISENBUD, A. Van de VEN, On the normal bundle of smooth rational space curves, Math. Ann., 256 (1981), 453-463. Zbl0443.14015MR83b:14002
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  7. [7] F. GHIONE, G. SACCHIERO, Normal bundles of rational curves. Manuscr. Math., 33 (1980), 111-128. Zbl0496.14021MR82b:14016
  8. [8] R. HARTSHORNE, Algebraic Geometry, Graduate Texts in Math., 52, Springer Verlag, New York, (1977), XVI + 496 p. Zbl0367.14001MR57 #3116
  9. [9] R. HARTSHORNE, Classification of Algebraic Space Curves, in "Vector Bundles and Differential Equations", Prog. in Math., 7, Birkhäuser, Boston, (1980), 83-112. Zbl0452.14005MR81m:14022
  10. [10] R. HARTSHORNE, A. HIRSCHOWITZ, Droites en position générale dans l'espace projectif, in "Algebraic Geometry", Proc. La Rabida 1981, Springer Lecture Notes in Math., 961, Springer Verlag (1982), 169-189. Zbl0555.14011MR85e:14043
  11. [11] R. HARTSHORNE, A. HIRSCHOWITZ, Smoothing Algebraic Space Curves, in Algebraic Geometry, Sitges 1983, Lecture Notes in Math., 1124 (1985), 98-131. Zbl0574.14028MR87h:14023
  12. [12] R. HARTSHORNE, A. HIRSCHOWITZ, Nouvelles courbes de bon genre via la cohomologie des faisceaux réflexifs, (en préparation). 
  13. [13] A. HIRSCHOWITZ, Sur la postulation générique des courbes rationnelles, Acta Math., 146 (1981), 209-230. Zbl0475.14027MR82j:14028
  14. [14] K. HULEK, The normal bundle of a curve on a quadric, Math. Ann., 258 (1981), 201-206. Zbl0458.14011MR83e:14034
  15. [15] D. PERRIN, Courbes passant par k points généraux de P3, C.R.A.S., 299 (1984), 451-453. Zbl0573.14008MR85j:14056
  16. [16] A. TANNENBAUM, Deformations of Space Curves, Arch. Math., Basel, 34 (1980), 37-42. Zbl0414.14016MR82k:14024
  17. [17] E. BALLICO, Ph. ELLIA, On the postulation of many disjoint rational curves in PN, N ≥ 4, Boll. U.M.I., à paraître. Zbl0591.14041
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  19. [19] E. BALLICO, Ph. ELLIA, Beyond the maximal rank conjecture for curves in P3, preprint n° 76, Nice, 1985. Zbl0556.14007

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