On the automorphisms of surfaces of general type in positive characteristic

Ballico, Edoardo

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993), p. 121-129 / Harvested from Biblioteca Digitale Italiana di Matematica

Access to full text
Full (PDF)
Full (DjVu)

Abstract
Résumé

Here we give an explicit polynomial bound (in term of $K_{X}^{2}$ and not depending on the prime $p$ ) for the order of the automorphism group of a minimal surface $X$ of general type defined over a field of characteristic $p > 0$ .

In questa Nota diamo una limitazione superiore esplicita di tipo polinomiale (in funzione solo di $K_{X}^{2}$ e non dipendente dal primo $p$ ) per l'ordine del gruppo degli automorfismi di una superficie generale $X$ definita su un campo di caratteristica $p > 0$ .

Publié le : 1993-06-01

MR 1233400 | Zbl 0795.14022

@article{RLIN_1993_9_4_2_121_0,
     author = {Edoardo Ballico},
     title = {On the automorphisms of surfaces of general type in positive characteristic},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {4},
     year = {1993},
     pages = {121-129},
     zbl = {0795.14022},
     mrnumber = {1233400},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1993_9_4_2_121_0}
}

Ballico, Edoardo. On the automorphisms of surfaces of general type in positive characteristic. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993) pp. 121-129. http://gdmltest.u-ga.fr/item/RLIN_1993_9_4_2_121_0/

Bibliographie

[1] Ballico, E. - Ciliberto, C., On Gaussian maps for projective varieties. In: Proceedings of the Cetraro Conference, to appear. | MR 1225587 | Zbl 0943.14019

[2] Beauville, A., Le nombre minimum de fibres singulières d'une courbe stable sur $P^{1}$ . In: Séminaire sur les pinceaux de courbes de genre au mois deux. Astérisque, vol. 86, 1980, 97-108. | Zbl 0502.14009

[3] Catanese, F. - Schneider, M., Bounds for stable bundles and degrees of Weierstrass schemes. Math. Ann., vol. 293, 1992, 579-594. | MR 1176022 | Zbl 0782.14016

[4] Corti, A., Polynomial bounds for the number of automorphisms of a surface of general type. Ann. scient. Ec. Norm. Sup., (4), vol. 24, 1991, 113-137. | MR 1088272 | Zbl 0758.14026

[5] Deligne, P. - Mumford, D., The irreducibility of the space of curves of given genus. Publ. Math. I.H.E.S., vol. 36, 1969, 75-110. | MR 262240 | Zbl 0181.48803

[6] Demazure, M. - Grothendieck, A., Schémas en Groupes, I (SGA 3, I). Lecture Notes in Math., 151, Springer-Verlag, 1970. | MR 274458 | Zbl 0207.51401

[7] Dixon, J. D., The structure of linear groups. Van Nostrand, London1971. | Zbl 0232.20079

[8] Ekedhal, T., Canonical models of surfaces of general type in positive characteristic. Publ. I.H.E.S., vol. 67, 1988, 97-144. | MR 972344 | Zbl 0674.14028

[9] Ganong, R. - Russell, P., The tangent bundle of a ruled surface. Math. Ann., vol. 271, 1985, 527-548. | MR 790114 | Zbl 0541.14035

[10] Howard, A. - Sommese, A. J., On the orders of the automorphism groups of certain projective manifolds. In: Manifolds and Lie Groups. Progress in Math., vol. 14, Birkhäuser, Boston-Basel-Stuttgart 1981, 145-158. | MR 642855 | Zbl 0483.32016

[11] Huckleberry, A. T. - Sauer, M., On the order of the automorphism group of a surface of general type. Math. Z , vol. 205, 1990, 321-329. | MR 1076138 | Zbl 0718.32022

[12] Igusa, J., Betti and Picard numbers of abstract algebraic surfaces. Proc. Nat. Acad. Sci. USA, vol. 46, 1960, 724-726. | MR 118725 | Zbl 0099.16402

[13] Kurke, H., Example of false ruled surfaces. In: Proceedings of Symposium on Algebraic Geometry Kinosaki, 1981, 203-223.

[14] Lang, W., Example of surfaces of general type with vector fields. In: Arithmetic and Geometry (papers dedicated to I. R. Shafarevich) Vol. 2. Progress in Math., vol. 36, Birkhäuser, Boston-Basel-Stuttgart1983, 167-173. | MR 717611 | Zbl 0576.14039

[15] Silverman, J., The arithmetic of elliptic curves. Graduate Text in Math., 106, Springer-Verlag, 1986. | MR 817210 | Zbl 0585.14026

[16] Xiao, G., On ahelian automorphism groups of a surface of general type. Invent. Math., vol. 102, 1990, 619-631. | Zbl 0739.14024

[17] Xiao, G., Bound of automorphisms of surfaces of general type, I. Preprint Max-Planck-Institut MPI/91-55. | MR 1259364 | Zbl 0811.14011