Picard group of hypersurfaces in toric 3-folds

Details Picard group of hypersurfaces in toric 3-folds Picard group of hypersurfaces in toric 3-folds

2010-11-03

arxiv.org/abs/1011.1003v3

Mathematics

Algebraic Geometry

14 pages. v2: some typos corrected. v3: Slightly changed title. Final version to appear in Int. J. Math., incorporates many (m

Scientific paper

10.1142/S0129167X12500280

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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