200,000 Terminal Toric Varieties of Picard Rank 2 for Machine Learning

200,000 randomly generated toric varieties of Picard rank 2 with at worst terminal singularities, in dimensions 2 to 10. The dataset was created by Tom Coates of Imperial College London and colleagues, as detailed in a 2023 Nature Communications paper. Each variety is represented by a (2 x N+2)-matrix stored in plain text files.

Use Cases

• Training machine learning models to predict the dimension of Fano varieties based on matrix representations.
• Analyzing the distribution of terminal singularities across different dimensions from 2 to 10.
• Benchmarking computational algebraic geometry algorithms against a large, generated corpus of toric varieties.

Strengths

• Contains 200,000 distinct mathematical objects, providing a substantial corpus for analysis.
• Covers a defined range of dimensions from 2 to 10, allowing for dimensional studies.
• Includes a direct link to the generating Magma code and a peer-reviewed paper for methodological context.

Limitations

• Column-level documentation is absent; field semantics must be inferred from the paper or code.
• Row count per dimension file is unknown, which may limit suitability assessment for specific dimensions.
• Last update date is unknown; freshness unverified.

Provenance

Source

Generated by Tom Coates, Alexander M. Kasprzyk, and Sara Veneziale; hosted on Zenodo.

Collection Method

Randomly generated using Magma code.