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      A Generalized Construction of Calabi-Yau Models and Mirror Symmetry

      1 , 2 , 3
      SciPost Physics
      Stichting SciPost

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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.

          Most cited references24

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          Phases of \(N=2\) Theories In Two Dimensions

          (2010)
          This is a study of the Landau-Ginzburg/Calabi-Yau correspondence, and related matters, using linear sigma models.
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            THE GEOMETRY OF TORIC VARIETIES

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              Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry

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                Author and article information

                Journal
                SciPost Physics
                SciPost Phys.
                Stichting SciPost
                2542-4653
                2018
                February 20 2018
                : 4
                : 2
                Affiliations
                [1 ]European Organization for Nuclear Research
                [2 ]University of New Hampshire
                [3 ]Howard University
                Article
                10.21468/SciPostPhys.4.2.009
                9356a4b7-404c-4729-a41c-b3bdd4420650
                © 2018

                This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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                Physics
                Physics

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