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Berglund-Hübsch-Krawitz mirrors via Shioda maps. (English) Zbl 1316.14076
The author discusses the birational geometry of BHK (Berglund-Hübsch-Krawitz) mirrors by using the Shioda map. Then, the birationality of certain Calabi-Yau orbifolds to finite quotients of a Fermat variety in a projective space is proven. Using this result, the author proves that if \(Z_{A,G}\) and \(Z_{A^{'},G^{'}}\) are certain Calabi-Yau orbifolds and if the groups \(G\) and \(G^{'}\) are equal, then the BHK mirrors \(Z_{A^{T},G^{T}}\) and \(Z_{(A^{'})^{T},(G^{'})^{T}}\) of these orbifolds are birational. Finally, the application of these results on an example is given.

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J33 Mirror symmetry (algebro-geometric aspects)
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