On linearly normal strange curves

Ballico, Edoardo

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993), p. 219-222 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

Here we prove a numerical bound implying that, except for smooth plane conics in characteristic 2, no complete linear system maps birationally a smooth curve into a projective space with a strange curve as image.

Si dimostra qui una diseguaglianza numerica che ha come applicazione il fatto che le coniche piane in caratteristica 2 corrispondono agli unici sistemi lineari completi su una curva liscia $X$ che determinano un morfismo birazionale $h$ da $X$ in uno spazio proiettivo con $h (X)$ curva «strana».

Publié le : 1993-09-01

MR 1250501 | Zbl 0818.14012

@article{RLIN_1993_9_4_3_219_0,
     author = {Edoardo Ballico},
     title = {On linearly normal strange curves},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {4},
     year = {1993},
     pages = {219-222},
     zbl = {0818.14012},
     mrnumber = {1250501},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1993_9_4_3_219_0}
}

Ballico, Edoardo. On linearly normal strange curves. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993) pp. 219-222. http://gdmltest.u-ga.fr/item/RLIN_1993_9_4_3_219_0/

Bibliographie

[1] Abramovich, D., Subvarieties of Abelian varieties and of Jacobians of curves. Ph. D. thesis, Harvard, April 1991. | MR 2686342

[2] Abramovich, D. - Harris, J., Abelian varieties and curves in $W_{d} (C)$ . Compositio Math., vol. 78, 1991, 227-238. | MR 1104789 | Zbl 0748.14010

[3] Arbarello, E. - Cornalba, M. - Griffiths, P. - Harris, J., Geometry of Algebraic Curves. Vol. I. Springer-Verlag, 1985. | MR 770932 | Zbl 0559.14017

[4] Ballico, E., On singular curves in the case of positive characteristic. Math. Nachr., vol. 141, 1989, 267-273. | MR 1014431 | Zbl 0699.14006

[5] Ballico, E. - Hefez, A., On the Galois group of a genetically etale morphism. Commun. Algebra, vol. 14, 1986, 899-909. | MR 834472 | Zbl 0593.14011

[6] Bayer, D. - Hefez, A., Strange plane curves. Commun. Algebra, vol. 19, 1991, 3041-3059. | MR 1132773 | Zbl 0756.14018

[7] Ciliberto, C., Hilbert functions of finite sets of points and genus of a curve in a projective space. In: Space Curves. Lecture notes in Mathematics, 1266, Springer-Verlag, 1987, 24-83. | MR 908707 | Zbl 0625.14016

[8] Coppens, M., A remark on curves covered by coverings. Proc. Amer. Math. Soc., to appear. | MR 1131033 | Zbl 0807.14021

[9] Ein, L., Stable vector bundles on projective spaces in char $p > 0$ . Math. Ann., vol. 254, 1980, 53-72. | MR 597836 | Zbl 0431.14003

[10] Eisenbud, D. - Harms, J., The dimension of the Chow variety of curves. Preprint. | Zbl 0780.14003

[11] Harris, J., Curve in a projective space. Les presses de L'Université de Montreal, 1982 (chapter III being joint work with D. Eisenbud). | MR 685427 | Zbl 0511.14014

[12] Laksov, D., Indecomposability of restricted tangent bundles. In: Tableaux de Young et foncteurs de Schur en algebre et géométrie. Astérisque, 87-88, 1981, 207-219. | MR 646821 | Zbl 0489.14008

[13] Lluis, E., Variedades algebraicas con ciertas conditiones en sur tangentes. Bol. Soc. Mat. Mexicana, s. 2, vol. 7, 1962, 47-56. | Zbl 0119.37101

[14] Rathmann, J., The uniform position principle for curves in characteristic $p$ . Math. Ann., vol. 276, 1987, 565-579. | MR 879536 | Zbl 0595.14041