A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list

• DOI: 10.1007/jhep02(2015)158
• Publication Date: 2015-02-26T05:45:09Z
• Authors: Ross Altman; James Gray; Yang-Hui He; Vishnu Jejjala; Brent D. Nelson
• Keywords: High Energy Physics - Theory; Nuclear and High Energy Physics; FOS: Physical sciences; 01 natural sciences; Mathematics - Algebraic Geometry; High Energy Physics - Theory (hep-th); 0103 physical sciences; FOS: Mathematics; QA; Algebraic Geometry (math.AG)

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��hler 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.