Families of Calabi-Yau hypersurfaces in \(\mathbb Q\)-Fano toric varieties. (English. French summary) Zbl 1353.14061
The authors prove that for a \(\mathbb{Q}\)-Fano toric variety \(X\) with canonical singularities and \(\Delta \in M_{\mathbb{Q}}\), a canonical polytope contained in the anticanonical polytope \(\theta\) of \(X\), a general hypersurface in \(\mathcal{F}_{\theta,\Delta^{*}}\) is a Calabi-Yau variety. Using this result, the authors provide a generalized Berglund-Hübsch-Krawitz transposition rule in which weighted projective space is replaced by a \(\mathbb{Q}\)-Fano toric variety with torsion free class group and canonical singularities.
Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale)
MSC:
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 14J33 | Mirror symmetry (algebro-geometric aspects) |
Keywords:
Calabi-Yau hypersurface; \(\mathbb{Q}\)-Fano, Berglund-Hübsch-Krawitz construction; canonical polytopeSoftware:
MagmaReferences:
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