Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds

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Gray, J.; Haupt, A.S.; Lukas, A.: Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds. In: Journal of High Energy Physics 2014 (2014), Nr. 9, 87. DOI: https://doi.org/10.1007/JHEP09(2014)093

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We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in ref. [1]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there are at least 36,779 topologically distinct manifolds in our list. We also study the fibration structure of these manifolds and find that 99.95 percent can be described as elliptic fibrations. In total, we find 50,114,908 elliptic fibrations, demonstrating the multitude of ways in which many manifolds are fibered. A sub-class of 26,088,498 fibrations satisfy necessary conditions for admitting sections. The complete data set can be downloaded here.
License of this version: CC BY 4.0 Unported
Document Type: article
Publishing status: publishedVersion
Issue Date: 2014
Appears in Collections:Fakultät für Mathematik und Physik

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1 image of flag of Germany Germany 50 98.04%
2 image of flag of Poland Poland 1 1.96%

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