Ravindra, G. V. ; Srinivas, V. (2009) The Noether-Lefschetz theorem for the divisor class group Journal of Algebra, 322 (9). pp. 3373-3391. ISSN 0021-8693
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Official URL: http://www.sciencedirect.com/science/article/pii/S...
Related URL: http://dx.doi.org/10.1016/j.jalgebra.2008.09.003
Abstract
Let X be a normal projective threefold over a field of characteristic zero and |L| be a base-point free, ample linear system on X. Under suitable hypotheses on (X,|L|), we prove that for a very general member Y ∈ |L|, 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 ⊂P3C of degree ≥ 4 has Pic(X) ≅ Z.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Divisor Class Group; Noether-Lefschetz Theorem |
| ID Code: | 58970 |
| Deposited On: | 02 Sep 2011 03:05 |
| Last Modified: | 02 Sep 2011 03:05 |
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