Mirror Symmetry Constructions

Part of the Trends in Mathematics book series (TM)


Mirror symmetry, in general, is a correspondence between objects of a certain type (manifolds, for example, or polynomial functions) and objects of a possibly different type that exchanges the “A-model” of each object with the “B-model” of its image. This equivalence has many manifestations in both mathematics and physics, but in order to discuss any of them, one must first understand how mirror pairs are constructed. We review three such constructions—the Batyrev construction, the Hori–Vafa construction, and the Berglund–Hubsch–Krawitz constructions—and, in each case, describe the A-model and B-model state spaces that mirror symmetry interchanges.



The authors would like to thank Mark Shoemaker for his detailed and valuable comments. Thanks are also due to Kentaro Hori for answering many of the authors’ questions, and to all of the students in the course on which these notes are based, without whom many corrections and clarifications would not have been made. The authors were partially supported by NSF RTG grant 1045119.


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Authors and Affiliations

  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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