A dataset of 200000 terminal toric varieties of Picard rank 2

DOI10.5281/zenodo.5790096Zenodo5790096MaRDI QIDQ6697830

Dataset published at Zenodo repository.

Author name not available (Why is that?)

Publication date: 5 January 2022

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 2to 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

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