On the automorphisms of surfaces of general type in positive characteristic

Edoardo Ballico

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 2, page 121-129
  • ISSN: 1120-6330

Abstract

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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 .

How to cite

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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 4.2 (1993): 121-129. <http://eudml.org/doc/244175>.

@article{Ballico1993,
abstract = {Here we give an explicit polynomial bound (in term of \( K^\{2\}\_\{X\} \) 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 \( p > 0 \).},
author = {Ballico, Edoardo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Algebraic surface; Automorphism group; Chern numbers; Surfaces of general type; subgroup of automorphism group; characteristic p; minimal surface of general type},
language = {eng},
month = {6},
number = {2},
pages = {121-129},
publisher = {Accademia Nazionale dei Lincei},
title = {On the automorphisms of surfaces of general type in positive characteristic},
url = {http://eudml.org/doc/244175},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Ballico, Edoardo
TI - On the automorphisms of surfaces of general type in positive characteristic
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/6//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 2
SP - 121
EP - 129
AB - Here we give an explicit polynomial bound (in term of \( K^{2}_{X} \) 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 \( p > 0 \).
LA - eng
KW - Algebraic surface; Automorphism group; Chern numbers; Surfaces of general type; subgroup of automorphism group; characteristic p; minimal surface of general type
UR - http://eudml.org/doc/244175
ER -

References

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  1. BALLICO, E. - CILIBERTO, C., On Gaussian maps for projective varieties. In: Proceedings of the Cetraro Conference, to appear. Zbl0943.14019MR1225587
  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. Zbl0502.14009
  3. CATANESE, F. - SCHNEIDER, M., Bounds for stable bundles and degrees of Weierstrass schemes. Math. Ann., vol. 293, 1992, 579-594. Zbl0782.14016MR1176022DOI10.1007/BF01444736
  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. Zbl0758.14026MR1088272
  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. Zbl0181.48803MR262240
  6. DEMAZURE, M. - GROTHENDIECK, A., Schémas en Groupes, I (SGA 3, I). Lecture Notes in Math., 151, Springer-Verlag, 1970. Zbl0207.51401MR274458
  7. DIXON, J. D., The structure of linear groups. Van Nostrand, London1971. Zbl0232.20079
  8. EKEDHAL, T., Canonical models of surfaces of general type in positive characteristic. Publ. I.H.E.S., vol. 67, 1988, 97-144. Zbl0674.14028MR972344
  9. GANONG, R. - RUSSELL, P., The tangent bundle of a ruled surface. Math. Ann., vol. 271, 1985, 527-548. Zbl0541.14035MR790114DOI10.1007/BF01456133
  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-Stuttgart1981, 145-158. Zbl0483.32016MR642855
  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. Zbl0718.32022MR1076138DOI10.1007/BF02571245
  12. IGUSA, J., Betti and Picard numbers of abstract algebraic surfaces. Proc. Nat. Acad. Sci. USA, vol. 46, 1960, 724-726. Zbl0099.16402MR118725
  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. Zbl0576.14039MR717611
  15. SILVERMAN, J., The arithmetic of elliptic curves. Graduate Text in Math., 106, Springer-Verlag, 1986. Zbl0585.14026MR817210
  16. XIAO, G., On ahelian automorphism groups of a surface of general type. Invent. Math., vol. 102, 1990, 619-631. Zbl0739.14024
  17. XIAO, G., Bound of automorphisms of surfaces of general type, I. Preprint Max-Planck-Institut MPI/91-55. Zbl0811.14011MR1259364DOI10.2307/2946627

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