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The Noether-Lefschetz theorem for the divisor class group

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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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
Publication: Journal of Algebra
Publisher: Elsevier Science
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.ac.in/id/eprint/24984

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