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On a criterion for hyperplane sections

Published online by Cambridge University Press:  24 October 2008

Lucian Bǎdescu
Lucian Bǎdescu
Affiliation:
Department of Mathematics, INCREST, 79622 Bucharest, Romania
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Extract

Throughout this paper we shall fix an algebraically closed field k. Consider the following:

Problem. Let (Y, L) be a normal polarized variety over k, i.e. a normal projective variety Y over k together with an ample line bundle L on Y. Then one may ask under which conditions the following statement holds:

(*) Every normal projective variety X containing Y as an ample Cartier divisor such that the normal bundle of Y in X is L, is isomorphic to the projective cone over Y.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 1 , January 1988 , pp. 59 - 67
Copyright
Copyright © Cambridge Philosophical Society 1988

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