Picard group of hypersurfaces in toric 3-folds

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.

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

References in corpus (3)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Lattice polarized toric K3 surfaces
• A remark on the Hard Lefschetz Theorem for Kähler orbifolds

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• Lattice duality for coupling pairs admitting polytope duality with trivial toric contribution
• The Noether--Lefschetz theorem in arbitrary characteristic
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