Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-17T05:21:46.753Z Has data issue: false hasContentIssue false
  • English
  • Français

Fibrations with moving cuspidal singularities

Published online by Cambridge University Press:  22 January 2016

Yoshifumi Takeda
Yoshifumi Takeda*
Affiliation:
Department of Mathematics, Nara Women’s University, Kita-Uoya Nishimachi, Nara 630, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let f: V → C be a fibration from a smooth projective surface onto a smooth projective curve over an algebraically closed field k. In the case of characteristic zero, almost all fibres of f are nonsingular. In the case of positive characteristic, it is, however, known that there exist fibrations whose general fibres have singularities. Moreover, it seems that such fibrations often have pathological phenomena of algebraic geometry in positive characteristic (see M. Raynaud [7], W. Lang [4]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 122 , June 1991 , pp. 161 - 179
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[1] Ekedahl, T., Canonical models of surfaces of general type in positive characteristic, Publ. Math. I.H.E.S., 67 (1988), 97–144.CrossRefGoogle Scholar
[2] Kurke, H., Example of false ruled surfaces, in Proceedings of Symposium on Algebraic Geometry Kinosaki, 1981, pp. 203–223.Google Scholar
[3] Lang, W. E., Quasi-elliptic surfaces in characteristic three, Ann. Sci. Ecole Norm. Sup., (4) 12 (1979), 473–500.Google Scholar
[4] Lang, W. E., Example of surface of general type with vector fields, in Arithmetic and Geometry, (Artin, M. and Tate, J. eds), Birkhäuser, 1983, pp. 167–173.Google Scholar
[5] Mukai, S., On counter-examples to the Kodaira Vanishing Theorem and the Yau inequality in positive characteristic (Japanese), in Proceedings of Symposium on Algebraic Geometry Kinosaki, 1979, pp. 9–31.Google Scholar
[6] Mumford, D., Some footnotes to the work of C. P. Ramanujam, in C. P. Rama-nujam-A Tribure, Springer, 1978, pp. 247–262.Google Scholar
[7] Raynaud, M., Contre-exemple au “Vanishing Theorem” en caractéristique p > 0, in C. P. Ramanujam-A Tribute, Springer, 1978, pp. 273–278.Google Scholar
[8] Rudakov, A. and Shafarevich, I., Inseparable morphisms of algebraic surfaces, Math. U.S.S.R. Izvestija, 10 (1976), 1205–1237.Google Scholar
[9] Seshadri, C. S., L’opération de Cartier. Applications. Séminaire C. Chevalley, 3iéme Année:1958/59-Variété de Picard, Exposé 6, Ecole Normale Supérieure, Secrétariat Mathématique, Paris, 1960.Google Scholar
[10] Szpiro, L., Le théorème de la régularité de l’adjointe de Gorenstein à Kodaira, in Proceedings of International Symposium on Algebraic Geometry Kyoto, (Nagata, M. ed), Kinokuniya, 1978, pp. 93–102.Google Scholar
[11] Szpiro, L., Sur le théorème de rigidité de Parsin et Arakelov, Astérisque, 64 (1979), 169–202.Google Scholar