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 Dimension from the Quantum Period, Tom Coates, Alexander M. Kasprzyk, and Sara Veneziale, 2022.

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

Files (9.9 MB)
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
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