Batyrev Mirror Symmetry

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 240)


We describe Batyrev’s construction of the mirror to a family of Calabi–Yau hypersurfaces in a Fano toric variety, based on polar duality for lattice polytopes. We revisit the example of the quintic threefold in this language, and briefly mention connections with later developments, such as the Batyrev–Borisov construction for complete intersections in Fano toric varieties, and the Gross–Siebert program.


Batyrev Lattice Polytope Toric Fano Varieties Polar Duality Quintic Threefolds 
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I am happy to thank the anonymous referee for useful comments and suggestions.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Pacific Institute for the Mathematical SciencesVancouverCanada

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