150,000 Terminal Weighted Projective Spaces in Dimensions 1 to 10

A dataset of 150,000 randomly generated weighted projective spaces with at worst terminal singularities, in dimensions 1 to 10. The data was created by Tom Coates of Imperial College London and is associated with a 2023 Nature Communications paper. Each data point is a sequence of weights defining a projective space.

Use Cases

• Training machine learning models to predict the dimension of a Fano variety based on weight sequences.
• Analyzing the distribution and properties of terminal weighted projective spaces across different dimensions.
• Benchmarking computational algebraic geometry algorithms against a large, generated corpus of examples.

Strengths

• Contains 150,000 distinct mathematical objects.
• Covers a range of dimensions from 1 to 10.
• Associated with a peer-reviewed publication in Nature Communications.

Limitations

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

Provenance

Source

Tom Coates, Alexander M. Kasprzyk, and Sara Veneziale via Imperial College London.

Collection Method

Randomly generated using Magma code.