All complete intersection Calabi-Yau four-folds. (English) Zbl 1342.14086

Summary: We present an exhaustive, constructive, classification of the Calabi-Yau fourfolds which can be described as complete intersections in products of projective spaces. A comprehensive list of 921,497 configuration matrices which represent all topologically distinct types of complete intersection Calabi-Yau four-folds is provided and can be downloadedhere. The manifolds have non-negative Euler characteristics in the range \(0 \leq \chi \leq 2610\). This data set will be of use in a wide range of physical and mathematical applications. Nearly all of these four-folds are elliptically fibered and are thus of interest for F-theory model building.


14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
Full Text: DOI arXiv


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[17] The original list of CICY three-folds found in ref. [1] can be downloaded at The list of complete intersection Calabi-Yau three-folds webpage, http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/cicylist/index.html.
[18] In its original format at CICY webpage, http://www.th.physik.uni-bonn.de/th/People/netah/cy/cicys/cicy.html.
[19] The full list of CICY four-fold configuration matrices and their Euler characteristics can be downloaded at All complete intersection Calabi-Yau four-folds webpage, http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html.
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