A Generalized Construction of Calabi-Yau Models and Mirror Symmetry

Abstract

We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. The associated non-reflexive and non-convex polytopes provide a generalization of Batyrev's original work, allowing us to construct novel pairs of mirror models. We showcase our proposal for this generalization by examining Calabi-Yau hypersurfaces in Hirzebruch n-folds, focusing on n=3,4 sequences, and outline the more general class of so-defined geometries.

29 pages, 6 figures. Typos corrected, references added, clarifications and an expanded appendix A following the comments by the referees (v.3)

References in corpus (3)

• On Calabi-Yau generalized complete intersections from Hirzebruch varieties and novel K3-fibrations
• A remark on generalized complete intersections
• More Toda-like (0,2) mirrors

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