Ugo Bruzzo, Antonella Grassi
Published 2010-11-03, updated 2011-10-05Version 3
We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.
Comments: 14 pages. v2: some typos corrected. v3: Slightly changed title. Final version to appear in Int. J. Math., incorporates many (mainly expository) changes suggested by the referee
Journal: Int. J. Math. 23, 1250028 (2012) [14 pages]
On the Picard group of low-codimension subvarieties
On the geometric genus of subvarieties of generic hypersurfaces
Determinantal quartics and the computation of the Picard group
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