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arXiv · 1611.10300

A Generalized Construction of Calabi-Yau Models and Mirror Symmetry

Per Berglund·Tristan Hubsch
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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.

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Per Berglund, Tristan Hubsch. 2016-11-30. A Generalized Construction of Calabi-Yau Models and Mirror Symmetry. https://doi.org/10.21468/scipostphys.4.2.009

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