Periods of the multiple Berglund-Huebsch-Krawitz mirrors
Alexander Belavin, Vladimir Belavin, Gleb Koshevoy
TL;DR
This paper investigates the periods of holomorphic forms in the context of Berglund-Hübsch-Krawitz mirror symmetry, demonstrating their coincidence for certain Calabi-Yau orbifolds related by BHK mirror pairs.
Contribution
It establishes that for loop-chain type Calabi-Yau pairs in the same weighted projective space, their periods of the holomorphic form are identical, advancing understanding of mirror symmetry.
Findings
Periods of holomorphic forms coincide for BHK mirror pairs.
Supports the consistency of mirror symmetry in specific Calabi-Yau configurations.
Provides a mathematical foundation for period comparisons in BHK mirror symmetry.
Abstract
We consider the multiple Calaby-Yau (CY) mirror phenomenon which appears in Berglund-H\"ubsch-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 manifolds in the same weighted projective space the periods of the holomorphic nonvanishing form coincide.
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Taxonomy
TopicsGeometry and complex manifolds · Molecular spectroscopy and chirality · Advanced Algebra and Geometry