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

Altman, R., Gray, J., He, Y., Jejjala, V. & Nelson, B. D. (2014). A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List. Journal of High Energy Physics, 2015(2), p. 158. doi: 10.1007/JHEP02(2015)158

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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 [1]. 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 Kähler 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.

Item Type: Article
Uncontrolled Keywords: Differential and Algebraic Geometry, Superstring Vacua
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/12854

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