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arXiv · 1411.1418

A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List

Ross Altman·James Gray·Yang-Hui He·Vishnu Jejjala·Brent D. Nelson
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Abstract

Kreuzer and Skarke famously produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions. These polyhedra describe the singular limits of ambient toric varieties in which Calabi-Yau threefolds can exist as hypersurfaces. In this paper, we review how to extract topological and geometric information about Calabi-Yau threefolds using the toric construction, and we provide, in a companion online database (see http://nuweb1.neu.edu/cydatabase), a detailed inventory of these quantities which are of interest to physicists. Many of the singular ambient spaces described by the Kreuzer-Skarke list can be smoothed out into multiple distinct toric ambient spaces describing different Calabi-Yau threefolds. We provide a list of the different Calabi-Yau threefolds which can be obtained from each polytope, up to current computational limits. We then give the details of a variety of quantities associated to each of these Calabi-Yau such as Chern classes, intersection numbers, and the K\"ahler and Mori cones, in addition to the Hodge data. This data forms a useful starting point for a number of physical applications of the Kreuzer-Skarke list.

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Ross Altman, James Gray, Yang-Hui He, Vishnu Jejjala, Brent D. Nelson. 2014-11-05. A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List. https://doi.org/10.1007/jhep02(2015)158

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