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On Curves and Surfaces with Projectively Equivalent Hyperplane Sections

Published online by Cambridge University Press:  20 November 2018

S. L'Vovsky
S. L'Vovsky*
Affiliation:
Profsoyuznaya ul, 20/9, kv.162. Russia, 117292 Moscow e-mail:, [email protected]
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Abstract

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In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we make some remarks on connections between the mentioned property of a projective variety and its adjunction properties.

Keywords

14D05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 384 - 392
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Ballico, E., On projective varieties with projectively equivalent zero-dimensional linear sections, Canad. J. Math. 35(1992), 3–13.Google Scholar
2. Ballico, E. and Hefez, A., On the Galios group associated to a generically étale morphism, Comm. Algebra 14(1986), 899–909.Google Scholar
3. Deligne, P. and Katz, N., Groupes de monodromie en géométrie algébrique, Lecture Notes in Math. 340, Springer, Berlin, 1973.Google Scholar
4. Fano, G., Sulle superficie dello spazio S3 a sezioni plane collineari, Rend R. Accad. Lincei (6a) 1(1925), 473–477.Google Scholar
5. Fano, G., Sulle superficie di uno spazio qualunque a sezioni iperpiane collineari, Rend R. Accad. Lincei (6°) 2(1925), 115–129.Google Scholar
6. Fubini, G., Sulle varietà a sezioni plane collineari, Rend R. Accad. Lincei (6a) 1(1925), 469–473.Google Scholar
7. L'vovsky, S., Extensions of projective varieties and deformations I, Michigan Math. J. 39(1992), 41–51.Google Scholar
8. L'vovsky, S., Extensions of projective varieties and deformations II, Michigan Math. J. 39(1992), 65–70.Google Scholar
9. Pardini, R., Some remarks on projective varieties with projectively equivalent hyperplane sections, Université di Pisa, 1992, preprint.Google Scholar
10. 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.Google Scholar
11. Zak, F. L., Surfaces with zero Lefschetz cycles, Russian, Mat. Zametki 13(1973), 869–880.Google Scholar