On montre que la réunion générale d’une courbe rationnelle avec des droites dans est de rang maximum.
The general union of a rational curve and lines in is proven to be of maximal rank.
@article{AIF_1985__35_4_39_0,
author = {Hartshorne, Robin and Hirschowitz, Andr\'e},
title = {Courbes rationnelles et droites en position g\'en\'erale},
journal = {Annales de l'Institut Fourier},
volume = {35},
year = {1985},
pages = {39-58},
doi = {10.5802/aif.1027},
mrnumber = {87e:14028},
zbl = {0565.14013},
language = {fr},
url = {http://dml.mathdoc.fr/item/AIF_1985__35_4_39_0}
}
Hartshorne, Robin; Hirschowitz, André. Courbes rationnelles et droites en position générale. Annales de l'Institut Fourier, Tome 35 (1985) pp. 39-58. doi : 10.5802/aif.1027. http://gdmltest.u-ga.fr/item/AIF_1985__35_4_39_0/
[1] , , Generic curves of small genus have maximal rank, Math. Ann., 264 (1983), 211-225. | Zbl 0501.14017
[2] , , Sur la postulation des courbes de Pn et de leurs projections, C.R.A.S., 299 (1984), 237-240. | Zbl 0565.14012
[3] , , The maximal rank conjecture for non special curves in P3, Invent. Math., 79 (1985), 541-555. | Zbl 0556.14007
[4] , , Divisors on general curves and cuspidal rational space curves, Invent. Math., (1983), 371-418. | MR 85h:14019 | Zbl 0527.14022
[5] , , On the normal bundle of smooth rational space curves, Math. Ann., 256 (1981), 453-463. | MR 83b:14002 | Zbl 0443.14015
[6] , Algebraic families on an algebraic surface, Amer. J. of Math., 90 (1968), 511-521. | MR 38 #5778 | Zbl 0176.18401
[7] , , Normal bundles of rational curves. Manuscr. Math., 33 (1980), 111-128. | MR 82b:14016 | Zbl 0496.14021
[8] , Algebraic Geometry, Graduate Texts in Math., 52, Springer Verlag, New York, (1977), XVI + 496 p. | MR 57 #3116 | Zbl 0367.14001
[9] , Classification of Algebraic Space Curves, in "Vector Bundles and Differential Equations", Prog. in Math., 7, Birkhäuser, Boston, (1980), 83-112. | MR 81m:14022 | Zbl 0452.14005
[10] , , 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 85e:14043 | Zbl 0555.14011
[11] , , Smoothing Algebraic Space Curves, in Algebraic Geometry, Sitges 1983, Lecture Notes in Math., 1124 (1985), 98-131. | MR 87h:14023 | Zbl 0574.14028
[12] , , Nouvelles courbes de bon genre via la cohomologie des faisceaux réflexifs, (en préparation).
[13] , Sur la postulation générique des courbes rationnelles, Acta Math., 146 (1981), 209-230. | MR 82j:14028 | Zbl 0475.14027
[14] , The normal bundle of a curve on a quadric, Math. Ann., 258 (1981), 201-206. | MR 83e:14034 | Zbl 0458.14011
[15] , Courbes passant par k points généraux de P3, C.R.A.S., 299 (1984), 451-453. | MR 85j:14056 | Zbl 0573.14008
[16] , Deformations of Space Curves, Arch. Math., Basel, 34 (1980), 37-42. | MR 82k:14024 | Zbl 0414.14016
[17] , , On the postulation of many disjoint rational curves in PN, N ≥ 4, Boll. U.M.I., à paraître.
[18] , On the postulation of disjoint rational curves in a projective space, Preprint Pisa, 1984.
[19] , , Beyond the maximal rank conjecture for curves in P3, preprint n° 76, Nice, 1985.