no. 4
Courbes rationnelles et droites en position générale
Annales de l'Institut Fourier, Tome 35 (1985) no. 4, pp. 39-58.

On montre que la réunion générale d’une courbe rationnelle avec des droites dans P 3 est de rang maximum.

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

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     title = {Courbes rationnelles et droites en position g\'en\'erale},
     journal = {Annales de l'Institut Fourier},
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Hartshorne, Robin; Hirschowitz, André. Courbes rationnelles et droites en position générale. Annales de l'Institut Fourier, Tome 35 (1985) no. 4, pp. 39-58. doi : 10.5802/aif.1027. http://www.numdam.org/articles/10.5802/aif.1027/

[1] E. Ballico, Ph. Ellia, Generic curves of small genus have maximal rank, Math. Ann., 264 (1983), 211-225. | EuDML | Zbl

[2] E. Ballico, Ph. Ellia, Sur la postulation des courbes de Pn et de leurs projections, C.R.A.S., 299 (1984), 237-240. | Zbl

[3] E. Ballico, Ph. Ellia, The maximal rank conjecture for non special curves in P3, Invent. Math., 79 (1985), 541-555. | EuDML | Zbl

[4] D. Eisenbud, J. Harris, Divisors on general curves and cuspidal rational space curves, Invent. Math., (1983), 371-418. | EuDML | MR | Zbl

[5] D. Eisenbud, A. Van De Ven, On the normal bundle of smooth rational space curves, Math. Ann., 256 (1981), 453-463. | EuDML | MR | Zbl

[6] J. Fogarty, Algebraic families on an algebraic surface, Amer. J. of Math., 90 (1968), 511-521. | MR | Zbl

[7] F. Ghione, G. Sacchiero, Normal bundles of rational curves. Manuscr. Math., 33 (1980), 111-128. | EuDML | MR | Zbl

[8] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math., 52, Springer Verlag, New York, (1977), XVI + 496 p. | MR | Zbl

[9] R. Hartshorne, Classification of Algebraic Space Curves, in "Vector Bundles and Differential Equations", Prog. in Math., 7, Birkhäuser, Boston, (1980), 83-112. | MR | Zbl

[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. | MR | Zbl

[11] R. Hartshorne, A. Hirschowitz, Smoothing Algebraic Space Curves, in Algebraic Geometry, Sitges 1983, Lecture Notes in Math., 1124 (1985), 98-131. | MR | Zbl

[12] R. Hartshorne, A. Hirschowitz, Nouvelles courbes de bon genre via la cohomologie des faisceaux réflexifs, (en préparation).

[13] A. Hirschowitz, Sur la postulation générique des courbes rationnelles, Acta Math., 146 (1981), 209-230. | MR | Zbl

[14] K. Hulek, The normal bundle of a curve on a quadric, Math. Ann., 258 (1981), 201-206. | MR | Zbl

[15] D. Perrin, Courbes passant par k points généraux de P3, C.R.A.S., 299 (1984), 451-453. | MR | Zbl

[16] A. Tannenbaum, Deformations of Space Curves, Arch. Math., Basel, 34 (1980), 37-42. | MR | Zbl

[17] E. Ballico, Ph. Ellia, On the postulation of many disjoint rational curves in PN, N ≥ 4, Boll. U.M.I., à paraître.

[18] E. Ballico, On the postulation of disjoint rational curves in a projective space, Preprint Pisa, 1984.

[19] E. Ballico, Ph. Ellia, Beyond the maximal rank conjecture for curves in P3, preprint n° 76, Nice, 1985.

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