Ravindra, GV and Srinivas, V
(2009)
*The Noether-Lefschetz theorem for the divisor class group.*
In: Journal of Algebra, 322
(9, Sp.).
pp. 3373-3391.

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## Abstract

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Item Type: | Journal Article |
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Additional Information: | Copyright for this article belongs to Elsevier Science. |

Keywords: | Divisor class group; Noether-Lefschetz theorem |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 04 Dec 2009 08:46 |

Last Modified: | 19 Sep 2010 05:52 |

URI: | http://eprints.iisc.ernet.in/id/eprint/24984 |

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