Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T23:12:10.001Z Has data issue: false hasContentIssue false
  • English
  • Français

On Projective Varieties with Projectively Equivalent Zero-Dimensional Linear Sections

Published online by Cambridge University Press:  20 November 2018

E. Ballico
E. Ballico*
Affiliation:
Department of Mathematics University of Trento 38050 Povo (TN) Italy
Rights & Permissions [Opens in a new window]

Abstract

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.

Here we give a partial classification of varieties X ⊂ Pn such that any two general zero-dimensional linear sections are projectively equivalent. They exist (with deg(X) > codim(X) + 2) only in positive characteristic.

Keywords

14N0514H99.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 3 - 13
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Andreatta, M. and Ballico, E., On the adjunction process over a surface in char, p, Manuscripta Math. 62(1988),227–244.Google Scholar
2. Andreatta, M. and Ballico, E., Classification of projective surfaces with small section genus: char, p ≥ 0, Rend. Sem. Mat. Univ. Padova, 84(1990),175–193.Google Scholar
3. Ballico, E., On singular curves in the case of positive characteristic, Math. Nachr. 141(1989),267–273.Google Scholar
4. Ballico, E., On the general hyperplane section of a curve in char, p, preprint.Google Scholar
5. Ballico, E. and Hefez, A., Non reflexive projective curves of low degree, Manuscripta Math. 70(1991),385–396.Google Scholar
6. Bayer, V. and Hefez, A., Strange curves, Comm. in Algebra (to appear).Google Scholar
7. Beauville, A., Sur les hypersurfaces dont les sections hyperplanes sont à module constant, in: The Grothendieck Festschrift, pp. 121-133, Birkhauser (1990).Google Scholar
8. Dale, M., Seven's theorem on the Veronese-surface, J. London Math. Soc. (2) 32(1985),419–425.Google Scholar
9. Ein, L., Varieties with small dual varieties I, Invent, math. 86(1986),63–74.Google Scholar
10. Ein, L., Varieties with small dual varieties II, Duke Math. J. 52(1985),895–907.Google Scholar
11. Hartshorne, R., Algebraic Geometry, Springer-Verlag, New York, Heidelberg, Berlin, 1977.Google Scholar
12. Homma, M., Funny plane curves in characteristic p > O, Comm. Algebra 15(1987),1469–1501.+O,+Comm.+Algebra+15(1987),1469–1501.>Google Scholar
13. Jouanolou, J. P., Theorems de Bertini et Applications, Progr. in Math. 42 Birkauser (1983).Google Scholar
14. Kaji, H., On the Gauss map of space curves in characteristic p, Compositio Math. 70(1989),177–197.Google Scholar
15. Kaji, H., Characterization of space curves with inseparable Gauss maps in extremal cases, preprint.Google Scholar
16. Katz, N., Pinceaux de Lefschetz: théorème de existence, in: SGA 7 II, Exposé XVII, Lect. Notes in Math. 340, Springer-Verlag, New York, Heidelberg, Berlin, 1973.Google Scholar
17. Kleiman, S., Tangency and duality, in: Proc. 1984 Vancouver Converence in Algebraic Geometry, pp. 163— 226, CMS-AMS Conference Proceedings, 6(1985).Google Scholar
18. Kleiman, S., Multiple tangents of smooth plane curves (after Kaji), preprint MIT, 1989.Google Scholar
19. Laksov, D., Indecomposability of restricted tangent bundles, in: Tableaux de Young et foncteurs de Schur en algèbre et géométrie, Astérisque 87-88(1981),207–219.Google Scholar
20. Rathmann, J., The uniform position principle for curves in characteristic p, Math. Ann. 276(1987),565–579.Google Scholar
21. Wallace, A., Tangency and duality over arbitrary fields, Proc. London Math. Soc. (3) 6(1956),321–342.Google Scholar
22. Zak, F. L., Projections of algebraic varieties, Math. USSR Sbornik 44(1983),535–544.Google Scholar