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A proof of the birationality of certain BHK-mirrors. (English) Zbl 1320.32032
Summary: We generalize and give an elementary proof of T. L. Kelly’s refinement [Adv. Theor. Math. Phys. 17, No. 6, 1425–1449 (2013; Zbl 1316.14076)] of M. Shoemaker’s result [Commun. Math. Phys. 331, No. 2, 417–429 (2014; Zbl 1395.14034)] on the birationality of certain BHK-mirrors. Our approach uses a construction that is equivalent to the generalization of M. Krawitz [FJRW rings and Landau-Ginzburg mirror symmetry. Ann Arbor, MI: ProQuest LLC, University of Michigan (PhD Thesis) (2010)] of the duality in [P. Berglund and T. Hübsch, in: Essays on mirror manifolds. Cambridge, MA: International Press. 388-407 (1992; Zbl 0842.32023)].

32Q25 Calabi-Yau theory (complex-analytic aspects)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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