| P. Berglund and T. Hubsch, A Generalized Construction of Mirror Manifolds, Nucl. Phys. B393 (1993) 377--391. |
....of the mirror manifold. There are known examples which do not have mirror manifolds. Earlier constructions of mirror manifolds exploits finite group automorphisms and only apply to some special Calabi Yau manifolds, see e.g. Greene Plesser [12] Greene Plesser Roan [13] Berglund Hubsch [3], etc. Batyrev [2] proposed a construction for Calabi Yau hypersurfaces in toric varieties. A general method of constructing mirror manifolds, suggested by the membrane theory in high energy physics, is proposed by Strominger, Yau and Zaslow [27] It RATIONAL HOMOTOPY TYPES OF MIRROR MANIFOLDS 3 ....
P. Berglund, T. Hubsch, A generalized construction of mirror manifolds, Nuclear Phys. B 393 (1993), no. 1-2, 377--391. Also in [34], 388-407.
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P. Berglund and T. Hubsch, A Generalized Construction of Mirror Manifolds, Nucl. Phys. B393 (1993) 377--391.
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