Dataset Open Access
A dataset of 200000 terminal toric varieties of Picard rank 2
Coates, Tom;
Kasprzyk, Alexander;
Veneziale, Sara
Toric varieties of Picard rank 2 with at worst terminal singularities
A dataset of 200000 randomly generated toric varieties of Picard rank 2 with at worst terminal Q-factorial singularities, in dimensions 2 to 10.
The data consists of the plain text files "rank_2_dim_N.txt" where N, which is the dimension of the toric variety, is in the range 2 to 10. Each line of the file specifies the entries of a (2 x N+2)-matrix. For example, the first line of "rank_2_dim_4.txt" is:
[[1,3,5,4,1,0],[0,1,2,5,3,1]]
and this corresponds to the 4-dimensional toric variety with weight matrix
1 3 5 4 1 0
0 1 2 5 3 1
and stability condition given by the sum of the columns, which in this case is
14
12
For details, see the paper:
"Machine learning the dimension of a Fano variety", Tom Coates, Alexander M. Kasprzyk, and Sara Veneziale, Nature Communications, 14:5526 (2023). doi:10.1038/s41467-023-41157-1
Magma code capable of generating this dataset is in the file "generate_rank_2.m".
If you make use of this data, please cite the above paper and the DOI for this data:
doi:10.5281/zenodo.5790096
| Name | Size | |
|---|---|---|
|
generate_rank_2.m
md5:38157918fe1fd564bd9f79306d69d5b9 |
3.9 kB | Download |
|
LICENSE
md5:65d3616852dbf7b1a6d4b53b00626032 |
7.0 kB | Download |
|
rank_2_dim_10.txt
md5:34dfad995ca01faee0b158e129250130 |
2.8 MB | Download |
|
rank_2_dim_2.txt
md5:60624584fb07a3e9dfd1b61417900267 |
44 Bytes | Download |
|
rank_2_dim_3.txt
md5:6cc7b9dead08424c733d5d735be8ba19 |
442 Bytes | Download |
|
rank_2_dim_4.txt
md5:6e139b229862deb0da1f40cdcbcd7be9 |
22.7 kB | Download |
|
rank_2_dim_5.txt
md5:aa81478d198e84e64358259411aef032 |
206.9 kB | Download |
|
rank_2_dim_6.txt
md5:0a59a4bda34e46878e18ecc06109856b |
771.2 kB | Download |
|
rank_2_dim_7.txt
md5:0d7ce176c89d22dbb25a6bf65aecced6 |
1.6 MB | Download |
|
rank_2_dim_8.txt
md5:2598ff7f53470b68265a8ec54ebd4f2b |
2.1 MB | Download |
|
rank_2_dim_9.txt
md5:f73d4be593333bd6354ebd0205046632 |
2.5 MB | Download |
|
README.txt
md5:183f32f0111c16a1f29810ceb7fbbeda |
1.1 kB | Download |
| All versions | This version | |
|---|---|---|
| Views | 76 | 76 |
| Downloads | 84 | 84 |
| Data volume | 64.8 MB | 64.8 MB |
| Unique views | 63 | 63 |
| Unique downloads | 46 | 46 |
- Publication date:
- January 5, 2022
- DOI:
-
- Keyword(s):
- Toric variety Geometry
- Grants:
-
European Commission:
- GWT - Gromov-Witten Theory: Mirror Symmetry, Birational Geometry, and the Classification of Fano Manifolds (682603)
-
EPSRC Centre for Doctoral Training in Geometry and Number Theory at the Interface (EP/L015234/1)
-
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