Calabi-Yau Complete Intersections in fake weighted projective spaces

This record contains all Calabi-Yau complete intersections of dimension up to five arising from nef-partitions in fake weighted projective spaces.

The files are named `CYCI_d_s.jsonl`, where $d$ corresponds to the dimension and $s$ to the codimension of the complete intersections. Each entry is stored as a triple `[Q, mu, md]` defined as follows:

• Q: The degree matrix of the ambient fake weighted projective space $Z$ (columns correspond to the classes of the torus-invariant prime divisors of $Z$).
• mu: An integer vector indicating the torsion orders of the class group of $Z$, represented in invariant factor form.
• md: An integer vector indicating the multidegree of the relations.

In the case of $3$-dimensional families, an additional fourth component `hd` is included, listing the Hodge numbers $(h_{1,1},h_{2,1})$ and the Euler characteristic.

We omit the $5$-dimensional Calabi-Yau hypersurfaces to limit file size, noting that this data is redundant with the classification of 6-dimensional reflexive simplices.

The data were generated using the algorithm described in the accompanying article.