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Picard group of hypersurfaces in toric 3-folds

Ugo Bruzzo·Antonella Grassi
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Abstract

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.

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Ugo Bruzzo, Antonella Grassi. 2011-10-05. Picard group of hypersurfaces in toric 3-folds. https://doi.org/10.1142/s0129167x12500280

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