Dataset Open Access
Regularized quantum periods for four-dimensional Fano manifolds
Coates, Tom;
Kasprzyk, Alexander
The database smooth_fano_4
This is a database of regularized quantum periods for four-dimensional Fano manifolds. The database will be updated as new four-dimensional Fano manifolds are discovered and new regularized quantum periods computed.
Each entry in the database is a key-value record with keys and values as described in the paper [CK2021]. If you make use of this data, please cite that paper and the DOI for this data:
doi:10.5281/zenodo.5708307
Names
The database describes Fano varieties via names, as follows:
| Name | Description |
|---|---|
| P1 | one-dimensional projective space |
| P2 | two-dimensional projective space |
| dP(k) | the del Pezzo surface of degree k given by the blow-up of P2 in 9-k points |
| P3 | three-dimensional projective space |
| Q3 | a quadric hypersurface in four-dimensional projective space |
| B(3,k) | the three-dimensional Fano manifold of Picard rank 1, Fano index 2, and degree 8k |
| V(3,k) | the three-dimensional Fano manifold of Picard rank 1, Fano index 1, and degree k |
| MM(r,k) | the k-th entry in the Mori-Mukai list of three-dimensional Fano manifolds of Picard rank r, ordered as in [CCGK2016] |
| P4 | four-dimensional projective space |
| Q4 | a quadric hypersurface in five-dimensional projective space |
| FI(4,k) | the four-dimensional Fano manifold of Fano index 3 and degree 81k |
| V(4,k) | the four-dimensional Fano manifold of Picard rank 1, Fano index 2, and degree 16k |
| MW(4,k) | the k-th entry in Table 12.7 of [IP1999] of four-dimensional Fano manifolds of Fano index 2 and Picard rank greater than 1 |
| Obro(4,k) | the k-th four-dimensional Fano toric manifold in Obro's classification [O2007] |
| Str(k) | the k-th Strangeway manifold in [CGKS2020] |
| CKP(k) | the k-th four-dimensional Fano toric complete intersection in [CKP2015] |
| CKK(k) | the k-th four-dimensional Fano quiver flag zero locus in Appendix B of [K2019] |
A name of the form "S1 x S2", where S1 and S2 are names of Fano manifolds X1 and X2, refers to the product manifold X1 x X2.
References
[CCGK2016] Quantum periods for 3-dimensional Fano manifolds; Tom Coates, Alessio Corti, Sergey Galkin, Alexander M. Kasprzyk; Geometry and Topology 20 (2016), no. 1, 103-256.
[CGKS2020] Quantum periods for certain four-dimensional Fano manifolds; Tom Coates, Sergey Galkin, Alexander M. Kasprzyk, Andrew Strangeway; Experimental Math. 29 (2020), no. 2, 183-221.
[CK2021] Databases of quantum periods for Fano manifolds; Tom Coates, Alexander M. Kasprzyk; 2021.
[CKP2015] Four-dimensional Fano toric complete intersections; Tom Coates, Alexander M. Kasprzyk, Thomas Prince; Proc. Royal Society A 471 (2015), no. 2175, 20140704, 14.
[IP1999] Fano varieties; V.A. Iskovskikh, Yu. G. Prokhorov; Encyclopaedia Math. Sci. vol. 47, Springer, Berlin, 1999, 1-247.
[K2019] Four-dimensional Fano quiver flag zero loci; Elana Kalashnikov; Proc. Royal Society A 275 (2019), no. 2225, 20180791, 23.
[O2007] An algorithm for the classification of smooth Fano polytopes; Mikkel Obro; arXiv:0704.0049 [math.CO]; 2007.
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LICENSE
md5:65d3616852dbf7b1a6d4b53b00626032 |
7.0 kB | Download |
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README.txt
md5:45ed76e1c157048e1767277777926d8f |
3.0 kB | Download |
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smooth_fano_4.txt
md5:d2cc34f3d9867f54066a0a7efa289e30 |
19.0 MB | Download |
| All versions | This version | |
|---|---|---|
| Views | 110 | 110 |
| Downloads | 37 | 37 |
| Data volume | 492.9 MB | 492.9 MB |
| Unique views | 95 | 95 |
| Unique downloads | 32 | 32 |
- Publication date:
- November 17, 2021
- DOI:
-
- Keyword(s):
- Fano manifolds Regularized quantum period Mirror symmetry Geometry
- Grants:
-
European Commission:
- GWT - Gromov-Witten Theory: Mirror Symmetry, Birational Geometry, and the Classification of Fano Manifolds (682603)
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Classification, Computation, and Construction: New Methods in Geometry (EP/N03189X/1)
- The Combinatorics of Mirror Symmetry (EP/N022513/1)
- License (for files):
- Creative Commons Zero v1.0 Universal