Calabi-Yau database

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.


References in zbMATH (referenced in 23 articles , 1 standard article )

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  1. Lee, Nam-Hoon: (d)-semistable Calabi-Yau threefolds of type III (2020)
  2. Altman, Ross; Carifio, Jonathan; Halverson, James; Nelson, Brent D.: Estimating Calabi-Yau hypersurface and triangulation counts with equation learners (2019)
  3. Bull, Kieran; He, Yang-Hui; Jejjala, Vishnu; Mishra, Challenger: Getting CICY high (2019)
  4. Gray, James; Wang, Juntao: Jumping spectra and vanishing couplings in heterotic line bundle standard models (2019)
  5. Limonchenko, I. Yu.; Panov, T. E.; Chernykh, G. S.: (SU)-bordism: structure results and geometric representatives (2019)
  6. Alexandrov, Sergei; Banerjee, Sibasish; Longhi, Pietro: Rigid limit for hypermultiplets and five-dimensional gauge theories (2018)
  7. Braun, Andreas P.; Lukas, Andre; Sun, Chuang: Discrete symmetries of Calabi-Yau hypersurfaces in toric four-folds (2018)
  8. Cicoli, Michele; Ciupke, David; Mayrhofer, Christoph; Shukla, Pramod: A geometrical upper bound on the inflaton range (2018)
  9. He, Yang-Hui; Seong, Rak-Kyeong; Yau, Shing-Tung: Calabi-Yau volumes and reflexive polytopes (2018)
  10. Cicoli, Michele; Ciupke, David; Diaz, Victor A.; Guidetti, Veronica; Muia, Francesco; Shukla, Pramod: Chiral global embedding of fibre inflation models (2017)
  11. Garbagnati, Alice; van Geemen, Bert: A remark on generalized complete intersections (2017)
  12. He, Yang-Hui; Jejjala, Vishnu; Pontiggia, Luca: Patterns in Calabi-Yau distributions (2017)
  13. Lee, Nam-Hoon: Calabi-Yau threefolds with small (h^1,1)’s from Fano threefolds (2017)
  14. Long, Cody; McAllister, Liam; Stout, John: Systematics of axion inflation in Calabi-Yau hypersurfaces (2017)
  15. Paffenholz, Andreas: \textttpolyDB: a database for polytopes and related objects (2017)
  16. Anderson, Lara B.; Apruzzi, Fabio; Gao, Xin; Gray, James; Lee, Seung-Joo: A new construction of Calabi-Yau manifolds: generalized CICYs (2016)
  17. Anderson, Lara B.; Gao, Xin; Gray, James; Lee, Seung-Joo: Tools for CICYs in F-theory (2016)
  18. Blaszczyk, Michael; Oehlmann, Paul-Konstantin: Tracing symmetries and their breakdown through phases of heterotic ((2,2)) compactifications (2016)
  19. Cicoli, Michele; Muia, Francesco; Shukla, Pramod: Global embedding of fibre inflation models (2016)
  20. Nibbelin, Stefan Groot; Ruehle, Fabian: Line bundle embeddings for heterotic theories (2016)

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