Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-03T08:56:39.666Z Has data issue: false hasContentIssue false
  • English
  • Français

On ample divisors

Published online by Cambridge University Press:  22 January 2016

Lucian Bădescu
Lucian Bădescu*
Affiliation:
I.N.C.R.E.S.T. Bucharest, Department of Mathematics, B-dul Pacii 220, 77588 Bucharest, Romania
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.

In this paper we are dealing with the following problem: determine all normal (or smooth) projective varieties X over an algebraically closed field k supporting a given variety Y as an ample Cartier divisor.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 86 , June 1982 , pp. 155 - 171
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[ 1 ] Altman, A. and Kleiman, S., Introduction to Grothendieck duality theory, Springer Lect. Notes Math., 146 (1970).Google Scholar
[ 2 ] Bădescu, L., A remark on the Grothendieck-Lefschetz theorem about the Picard group, Nagoya Math. J., 71 (1978), 169–179.CrossRefGoogle Scholar
[ 3 ] Dieudonné, J. and Grothendieck, A., Eléments de Géométrie Algébrique, Publ. Math. IHES, 11 (1961).Google Scholar
[ 4 ] Grothendieck, A., Sur la classification des fibres holomorphes sur la sphere de Riemann, Amer. J. Math., 79 (1957), 121–138.CrossRefGoogle Scholar
[ 5 ] Grothendieck, A., Local cohomology, Springer Lect. Notes Math., 41 (1967).Google Scholar
[ 6 ] Grothendieck, A., Revetements étales et groupe fondamental, Springer Lect. Notes Math., 221 (1971).CrossRefGoogle Scholar
[ 7 ] Grothendieck, A., Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux, North-Holland, Amsterdam (1968).Google Scholar
[ 8 ] Hartshorne, R., Ample subvarieties of algebraic varieties, Springer Lect. Notes Math., 156 (1970).Google Scholar
[ 9 ] Hironaka, H., Smoothing of algebraic cycles of small dimensions, Amer. J. Math., 90 (1968), 1–54.Google Scholar
[10] Kleiman, S., Toward a numerical theory of ampleness, Annals Math., 84 (1966), 293–344.Google Scholar
[11] Kobayashi, S. and Ochiai, T., Characterizations of complex projective spaces and hyperquadrics, J. Math. Kyoto Univ., 13–1 (1973), 31–47.Google Scholar
[12] Mori, S., On a generalization of complete intersections, J. Math. Kyoto Univ., 15–3 (1975), 619–646.Google Scholar
[13] Sommese, A. J., On manifolds that cannot be ample divisors, Math. Ann., 221 (1976), 55–72.CrossRefGoogle Scholar