A dataset of 150000 terminal weighted projective spaces

Weighted projective spaces with at worst terminal singularities

A dataset of 150000 randomly generated weighted projective spaces with at worst terminal singularities, in dimensions 1 to 10.

The data consists of the plain text files "rank_1_dim_N.txt" where N, which is the dimension of the weighted projective space, is in the range 1 to 10. Each line of the file is a sequence of weights of length N+1. For example, the first line of "rank_1_dim_4.txt" is:

[1,2,5,14,21]

and this corresponds to the 4-dimensional weighted projective space P(1,2,5,14,21).

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_1.m".

If you make use of this data, please cite the above paper and the DOI for this data:

doi:10.5281/zenodo.5790079