Published January 5, 2022 | Version v1.0
Dataset Open

A dataset of 200000 terminal toric varieties of Picard rank 2

  • 1. Imperial College London
  • 2. University of Nottingham

Description

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 Communications14:5526 (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

Files

rank_2_dim_10.txt

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Additional details

Funding

EPSRC Centre for Doctoral Training in Geometry and Number Theory at the Interface EP/L015234/1
UK Research and Innovation
GWT – Gromov-Witten Theory: Mirror Symmetry, Birational Geometry, and the Classification of Fano Manifolds 682603
European Commission
Classification, Computation, and Construction: New Methods in Geometry EP/N03189X/1
UK Research and Innovation
The Combinatorics of Mirror Symmetry EP/N022513/1
UK Research and Innovation