We show that the usual sufficient criterion for a very general hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to quasi-smooth hypersurfaces in complete simplicial toric varieties. This sufficient condition always holds for very general K3 surfaces embedded in Fano toric 3-folds.
Picard group of hypersurfaces in toric 3-folds / Bruzzo, U.; Grassi, A.. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 23:2(2012). [10.1142/S0129167X12500280]
Picard group of hypersurfaces in toric 3-folds
Bruzzo, U.;
2012-01-01
Abstract
We show that the usual sufficient criterion for a very general hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to quasi-smooth hypersurfaces in complete simplicial toric varieties. This sufficient condition always holds for very general K3 surfaces embedded in Fano toric 3-folds.File in questo prodotto:
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