Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-13T13:50:17.900Z Has data issue: false hasContentIssue false
  • English
  • Français

Double covers of Pn as very ample divisors

Published online by Cambridge University Press:  22 January 2016

Antonio Lanteri ,
Marino Palleschi  and
Andrew J. Sommese
Antonio Lanteri
Affiliation:
Dipartimento di Matematica “F. Enriques”-Università, Via C. Saldini, 50 1-20133 Milano, Italy, LANTERI@VMIMAT.MAT.UNIMI.IT, APELLES@VMIMAT.MAT.UNIMI.IT
Marino Palleschi
Affiliation:
Dipartimento di Matematica “F. Enriques”-Università, Via C. Saldini, 50 1-20133 Milano, Italy, LANTERI@VMIMAT.MAT.UNIMI.IT, APELLES@VMIMAT.MAT.UNIMI.IT
Andrew J. Sommese
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, INDIANA 46556, U. S. A., sommese@hobbes.math.nd.edu
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.

The classical subject of surfaces containing a hyperelliptic curve (here a double cover of P1) among their hyperplane sections was settled some years ago by the third author and Van de Ven [SV] (see also [Se], [Io]). This paper is devoted to answering the following general question arising very naturally from that problem.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 137 , March 1995 , pp. 1 - 32
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

References

[Ba] Bādescu, L., On ample divisors, Nagoya Math. J., 86 (1982), 155–171.CrossRefGoogle Scholar
[Bar] Bardelli, F., Su alcune rigate razionali di dimensione tre minimali, Boll. Un. Mat. Ital., Suppl., 2 (1980), 229–241.Google Scholar
[BS] Beltrametti, M. C., Sommese, A. J., New properties of special varieties arising from adjunction theory, J. Math. Soc. Japan, 43 (1991), 381–412.Google Scholar
[BBS] Beltrametti, M., Biancofiore, A. and Sommese, A. J., Projective N-folds of log-general type I, Trans. Amer. Math. Soc, 314 (1989), 825–849.Google Scholar
[Be] Besana, G. M., On the geometry of quadric fibrations arising in adjunction theory, I, Preprint.Google Scholar
[H] Hartshorne, R., Algebraic Geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1977.Google Scholar
[Io] Ionescu, P., Ample and very ample divisors on a surface, Rev. Roum. Math. Pures Appl., 33 (1988), 349–358.Google Scholar
[I] Iskovskih, V., Fano 3-folds, I, Izv. Akad. Nauk. SSSR Ser. Mat, 41 (1977), 512–562; II. Ibid. 42 (1977), 469–506.Google Scholar
[LP] Lanteri, A., Palleschi, M., Characterizing projective bundles by means of ample divisors, Manuscripta Math., 45 (1984), 207–218.Google Scholar
[La] Lazarsfeld, R., Some applications of the theory of positive vector bundles, Complete Intersections, Acireale 1983, pp. 29–61. Lect. Notes Math., 1092, Springer-Verlag, Berlin, Heidelberg, New York, 1984.Google Scholar
[MM1] Mori, S., Mukai, S., Classification of Fano 3-folds with B2 > 2, Manuscripta Math., 36(1981), 147–162.Google Scholar
[MM2] Mori, S., On Fano 3-folds with B2 > 2, Algebraic Varieties and Analytic Varieties, pp. 101–129, Adv. Studies in Pure Math., 1, Kinokuniya, Tokyo, 1983.CrossRefGoogle Scholar
[Se] Serrano, F., The adjunction mapping and hyperelliptic divisors on a surface, J. reine angew. Math., 381 (1987), 90–109.Google Scholar
[SI] Sommese, A. J., Hyperplane sections of projective surfaces, I-The adjunction mapping, Duke Math. J., 46 (1979), 377–401.Google Scholar
[S2] Sommese, A. J., On the adjunction theoretic structure of projective varieties, Complex Analysis and Algebraic Geometry, Göttingen 1985, pp. 175–213. Lect. Notes Math., 1194. Springer Verlag, Berlin, Heidelberg, New York, 1986.Google Scholar
[S3] Sommese, A. J., On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold, J. reine angew. Math., 402 (1989), 211–220; erratum, ibid. 411 (1989), 122–123.Google Scholar
[SV] Sommese, A. J., Van de Ven, A., On the adjunction mapping, Math., Ann., 278 (1987), 593–603.Google Scholar