Picard group of hypersurfaces in toric 3-folds
Algebraic Geometry
2013-05-29 v3
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.
Cite
@article{arxiv.1011.1003,
title = {Picard group of hypersurfaces in toric 3-folds},
author = {Ugo Bruzzo and Antonella Grassi},
journal= {arXiv preprint arXiv:1011.1003},
year = {2013}
}
Comments
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