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.本数据集收录了所有来自伪加权射影空间中的nef-分划（nef-partitions）、维度不超过五的卡拉比-丘（Calabi-Yau）完全交形。 数据集文件的命名格式为`CYCI_d_s.jsonl`，其中$d$对应完全交形的维度，$s$对应其余维数。每个数据条目以三元组`[Q, mu, md]`存储，各分量定义如下： `Q`：环境伪加权射影空间$Z$的度矩阵，其列对应$Z$的环面不变素除子（torus-invariant prime divisors）的同调类。 `mu`：以不变因子形式（invariant factor form）表示的整数向量，用于指明空间$Z$的类群（class group）的挠阶数。 `md`：指明关系式多重次数的整数向量。 针对三维族数据集，会额外添加第四分量`hd`，用于列出霍奇数（Hodge numbers）$(h_{1,1},h_{2,1})$以及欧拉示性数（Euler characteristic）。 为控制文件体积，本数据集未收录五维卡拉比-丘超曲面；需说明，此类数据与6维自反单纯形（reflexive simplex）的分类结果存在冗余。 本数据集的生成算法详见配套学术文章。