Calabi-Yau database swMATH ID: 24665 Software Authors: Altman, Ross; Gray, James; He, Yang-Hui; Jejjala, Vishnu; Nelson, Brent D. Description: A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list. M. Kreuzer and H. Skarke [Adv. Theor. Math. Phys. 4, No. 6, 1209–1230 (2000; Zbl 1017.52007)] 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 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. Homepage: http://www.rossealtman.com/ Keywords: differential and algebraic geometry; superstring vacua Related Software: PALP; cohomCalg; SageMath; CICY Quotients; SINGULAR; GAP; STRINGVACUA; Magma; TOPCOM; polyDB; OEIS; Jupyter; MNIST; Bertini; Mathematica; Macaulay2; Fermat.m; fminsearch; Quiver; polymake_smooth_fano Cited in: 40 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list. Zbl 1388.53071Altman, Ross; Gray, James; He, Yang-Hui; Jejjala, Vishnu; Nelson, Brent D. 2015 all top 5 Cited by 72 Authors 8 Shukla, Pramod S. 6 He, Yang-Hui Evariste 5 Gray, James A. 4 Cicoli, Michele 3 Altman, Ross 3 Anderson, Lara B. 3 Gao, Xin 3 Jejjala, Vishnu 3 Lee, Namhoon 3 Nelson, Brent D. 3 Quevedo Rodriguez, Fernando 3 Valandro, Roberto 2 Braun, Andreas P. 2 Carifio, Jonathan 2 Carta, Federico 2 Ciupke, David 2 Crinò, Chiara 2 Junghans, Daniel 2 Lee, Seungjoo 2 Lukas, André 2 Mininno, Alessandro 2 Muia, Francesco 2 Wang, Juntao 1 Abdussalam, Shehu S. 1 Abel, Steven A. 1 Alexandrov, Sergei Yu. 1 Apruzzi, Fabio 1 Banerjee, Sibasish 1 Bao, Jiakang 1 Blaszczyk, Michael 1 Bull, Kieran 1 Chernykh, G. S. 1 Colverd, Grace Beaney 1 Diaz, Victor Alfonzo 1 Faraggi, Alon E. 1 Garbagnati, Alice 1 Graña, Mariana 1 Grimm, Thomas W. 1 Guidetti, Veronica 1 Halverson, James 1 Herráez, Alvaro 1 Hurtado Heredia, M. 1 Leontaris, George K. 1 Limonchenko, Ivan Yur’evich 1 Long, Cody 1 Longhi, Pietro 1 Marrani, Alessio 1 Mayrhofer, Christoph 1 McAllister, Liam 1 Mishra, Anshul 1 Mishra, Challenger 1 Nibbelin, Stefan Groot 1 Nibbelink, S. Groot 1 Oehlmann, Paul-Konstantin 1 Paffenholz, Andreas 1 Panov, Taras E. 1 Plauschinn, Erik 1 Pontiggia, Luca 1 Ruehle, Fabian 1 Rummel, Markus 1 Schachner, Andreas 1 Seong, Rak-Kyeong 1 Shiu, Gary 1 Staessens, Wieland 1 Stout, John 1 Sumitomo, Yoske 1 Sun, Chuang 1 Tripathy, Prasanta K. 1 Van De Heisteeg, Damian 1 van Geemen, Bert 1 Yau, Shing-Tung 1 Ye, Fang all top 5 Cited in 8 Serials 27 Journal of High Energy Physics 4 Nuclear Physics. B 3 Communications in Mathematical Physics 1 Physics Letters. B 1 Russian Mathematical Surveys 1 Manuscripta Mathematica 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Lecture Notes in Mathematics all top 5 Cited in 11 Fields 29 Quantum theory (81-XX) 20 Algebraic geometry (14-XX) 13 Relativity and gravitational theory (83-XX) 6 Differential geometry (53-XX) 5 Several complex variables and analytic spaces (32-XX) 3 Astronomy and astrophysics (85-XX) 2 Convex and discrete geometry (52-XX) 2 Algebraic topology (55-XX) 2 Computer science (68-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year