Abstract
We consider the multiple Calabi–Yau mirror phenomenon which appears in Berglund–Hübsch–Krawitz (BHK) mirror symmetry. We show that for any pair of Calabi–Yau orbifolds that are BHK mirrors of a loop–chain-type pair of Calabi–Yau threefolds in the same weighted projective space the periods of the holomorphic nonvanishing form coincide.
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Notes
With a slight abuse of notation, we use here h for the Hodge number of the orbifold, which we used before for the original manifold \(X_M\).
See also [19] for related discussion.
This was calculated using Mathematica, the algorithm is based on the definition of the polynomials \(W ^0_M\) of chain and loop types given above. First, we find all the cases for these two types separately, then the intersection of the two sets is found.
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Acknowledgements
The work of A. Belavin has been supported by the Russian Science Foundation under the grant 18-12-00439. The authors thank the reviewers for their careful reading and very helpful comments and remarks.
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In memory of Boris Dubrovin.
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Belavin, A., Belavin, V. & Koshevoy, G. Periods of the multiple Berglund–Hübsch–Krawitz mirrors. Lett Math Phys 111, 93 (2021). https://doi.org/10.1007/s11005-021-01439-5
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DOI: https://doi.org/10.1007/s11005-021-01439-5