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arxiv: 1011.1003 · v3 · pith:Z6KYZCNUnew · submitted 2010-11-03 · 🧮 math.AG

Picard group of hypersurfaces in toric 3-folds

Ugo Bruzzo , Antonella Grassi This is my paper
classification 🧮 math.AG
keywords toricfoldsgenerichypersurfacespicardsufficientalwaysambient
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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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  1. A result on the generic Picard number of surfaces in fake weighted projective 3-spaces

    math.AG 2026-04 unverdicted novelty 5.0

    A criterion is established for generic nondegenerate surfaces in fake weighted projective 3-spaces to have Picard number >1 via edge degenerations, genus tracking, and vanishing cohomology classes yielding an extra ra...