Perfect Cones

In a given dimension n, there exists only a finite number of orbits of perfect cones of rank k. This page provides data and references for their enumeration across several dimensions and ranks.

Research Highlights

Rank 9 Support: To analyze the perfect form compactification of A_g, we enumerated perfect cones of rank up to 9.
Lattice Correspondences: Perfect cones of dimension n and rank n correspond to specific configurations of shortest vectors.
Classifications:
- Dimensions n ≤ 9: Classification based on Minkowskian sublattices.
- Faces of cones (Dimension ≤ 7): Detailed enumeration available in our cohomology study.
- Rank 9, Dimension 8: Specific enumeration for the compactification of A_g.

References

Smoothness and singularities of the perfect form compactification of A_g
On classifying Minkowskian sublattices
Perfect forms and the cohomology of modular groups

Download Data

A merged dataset containing results from these investigations is available:

DATApaper.tar.gz

Note: Data can be read in GAP using the ReadAsFunction(File)() command.