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Patterns in Calabi-Yau distributions. (English) Zbl 1376.81059

Summary: We explore the distribution of topological numbers in Calabi-Yau manifolds, using the Kreuzer-Skarke dataset of hypersurfaces in toric varieties as a testing ground. While the Hodge numbers are well-known to exhibit mirror symmetry, patterns in frequencies of combination thereof exhibit striking new patterns. We find pseudo-Voigt and Planckian distributions with high confidence and exact fit for many substructures. The patterns indicate typicality within the landscape of Calabi-Yau manifolds of various dimension.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J33 Mirror symmetry (algebro-geometric aspects)
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