40 basic regular quotient singularity types and
52 irregular quotient singularity types
| Singularity type | Index |
|---|---|
| [48] | 24 |
| [29, 5] | 24 |
| [2, 13, 2] | 24 |
| [5, 10, 5] | 24 |
| [26, 7, 2] | 24 |
| [28, 2, 4] | 24 |
| [5, 7, 7, 2] | 24 |
| [5, 9, 2, 4] | 24 |
| [2, 7, 4, 7, 2] | 24 |
| [2, 8, 4, 2, 2] | 24 |
| [4, 2, 6, 7, 2] | 24 |
| [4, 2, 8, 2, 4] | 24 |
| [4, 4, 2, 2, 2] | 24 |
| [26, 2, 4, 2, 2] | 24 |
| [5, 7, 2, 4, 2, 2] | 24 |
| [27, 2, 2, 2, 2, 3] | 24 |
| [2, 2, 4, 3, 4, 2, 2] | 24 |
| [2, 7, 4, 2, 4, 2, 2] | 24 |
| [2, 8, 2, 3, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 5, 2, 2] | 24 |
| [4, 2, 6, 2, 4, 2, 2] | 24 |
| [5, 8, 2, 2, 2, 2, 3] | 24 |
| [26, 2, 2, 3, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 2, 5, 7, 2] | 24 |
| [4, 2, 7, 2, 2, 2, 2, 3] | 24 |
| [5, 7, 2, 2, 3, 2, 2, 2] | 24 |
| [2, 2, 4, 2, 4, 2, 4, 2, 2] | 24 |
| [2, 2, 4, 3, 2, 3, 2, 2, 2] | 24 |
| [2, 7, 4, 2, 2, 3, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 3, 3, 2, 2, 2] | 24 |
| [4, 2, 6, 2, 2, 3, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 2, 5, 2, 4, 2, 2] | 24 |
| [2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2] | 24 |
| [2, 2, 4, 2, 4, 2, 2, 3, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 2, 6, 2, 2, 2, 2, 3] | 24 |
| [3, 2, 2, 2, 2, 5, 2, 2, 3, 2, 2, 2] | 24 |
| [2, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 2] | 24 |
| [6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [26, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [5, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 7, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [4, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| Basic singularity type | Second singularity type | Third singularity type | Index |
|---|---|---|---|
| [25, 25] | [25, 2, 25] | [25, 2, 2, 25] | 24 |
| [25, 6, 5] | [25, 2, 6, 5] | [25, 2, 2, 6, 5] | 24 |
| [2, [2], [2], [13]] | [2, [2], [2], [2, 13]] | [2, [2], [2], [2, 2, 13]] | 24 |
| [5, 6, 6, 5] | [5, 6, 2, 6, 5] | [5, 6, 2, 2, 6, 5] | 24 |
| [25, 3, 7, 2] | [25, 2, 3, 7, 2] | [25, 2, 2, 3, 7, 2] | 24 |
| [25, 5, 2, 4] | [25, 2, 5, 2, 4] | [25, 2, 2, 5, 2, 4] | 24 |
| [3, [2], [2], [4, 2]] | [2, [2], [2], [3, 4, 2]] | [2, [2], [2], [2, 3, 4, 2]] | 24 |
| [4, [2], [2], [2, 3]] | [2, [2], [2], [4, 2, 3]] | [2, [2], [2], [2, 4, 2, 3]] | 24 |
| [5, 6, 3, 7, 2] | [5, 6, 2, 3, 7, 2] | [5, 6, 2, 2, 3, 7, 2] | 24 |
| [5, 6, 5, 2, 4] | [5, 6, 2, 5, 2, 4] | [5, 6, 2, 2, 5, 2, 4] | 24 |
| [2, 7, 3, 3, 7, 2] | [2, 7, 3, 2, 3, 7, 2] | [2, 7, 3, 2, 2, 3, 7, 2] | 24 |
| [4, 2, 5, 3, 7, 2] | [4, 2, 5, 2, 3, 7, 2] | [4, 2, 5, 2, 2, 3, 7, 2] | 24 |
| [4, 2, 5, 5, 2, 4] | [4, 2, 5, 2, 5, 2, 4] | [4, 2, 5, 2, 2, 5, 2, 4] | 24 |
| [25, 3, 2, 4, 2, 2] | [25, 2, 3, 2, 4, 2, 2] | [25, 2, 2, 3, 2, 4, 2, 2] | 24 |
| [5, 6, 3, 2, 4, 2, 2] | [5, 6, 2, 3, 2, 4, 2, 2] | [5, 6, 2, 2, 3, 2, 4, 2, 2] | 24 |
| [25, 4, 2, 2, 2, 2, 3] | [25, 2, 4, 2, 2, 2, 2, 3] | [25, 2, 2, 4, 2, 2, 2, 2, 3] | 24 |
| [2, 7, 3, 3, 2, 4, 2, 2] | [2, 7, 3, 2, 3, 2, 4, 2, 2] | [2, 7, 3, 2, 2, 3, 2, 4, 2, 2] | 24 |
| [4, 2, 5, 3, 2, 4, 2, 2] | [4, 2, 5, 2, 3, 2, 4, 2, 2] | [4, 2, 5, 2, 2, 3, 2, 4, 2, 2] | 24 |
| [5, 6, 4, 2, 2, 2, 2, 3] | [5, 6, 2, 4, 2, 2, 2, 2, 3] | [5, 6, 2, 2, 4, 2, 2, 2, 2, 3] | 24 |
| [25, 3, 2, 2, 3, 2, 2, 2] | [25, 2, 3, 2, 2, 3, 2, 2, 2] | [25, 2, 2, 3, 2, 2, 3, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 2, 4, 3, 7, 2] | [3, 2, 2, 2, 2, 4, 2, 3, 7, 2] | [3, 2, 2, 2, 2, 4, 2, 2, 3, 7, 2] | 24 |
| [4, 2, 5, 4, 2, 2, 2, 2, 3] | [4, 2, 5, 2, 4, 2, 2, 2, 2, 3] | [4, 2, 5, 2, 2, 4, 2, 2, 2, 2, 3] | 24 |
| [5, 6, 3, 2, 2, 3, 2, 2, 2] | [5, 6, 2, 3, 2, 2, 3, 2, 2, 2] | [5, 6, 2, 2, 3, 2, 2, 3, 2, 2, 2] | 24 |
| [2, 2, 4, 2, 3, 3, 2, 4, 2, 2] | [2, 2, 4, 2, 3, 2, 3, 2, 4, 2, 2] | [2, 2, 4, 2, 3, 2, 2, 3, 2, 4, 2, 2] | 24 |
| [2, 7, 3, 3, 2, 2, 3, 2, 2, 2] | [2, 7, 3, 2, 3, 2, 2, 3, 2, 2, 2] | [2, 7, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2] | 24 |
| [4, 2, 5, 3, 2, 2, 3, 2, 2, 2] | [4, 2, 5, 2, 3, 2, 2, 3, 2, 2, 2] | [4, 2, 5, 2, 2, 3, 2, 2, 3, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 2, 4, 3, 2, 4, 2, 2] | [3, 2, 2, 2, 2, 4, 2, 3, 2, 4, 2, 2] | [3, 2, 2, 2, 2, 4, 2, 2, 3, 2, 4, 2, 2] | 24 |
| [2, 2, 4, 2, 3, 3, 2, 2, 3, 2, 2, 2] | [2, 2, 4, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2] | [2, 2, 4, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 3] | [3, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 3] | [3, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 3] | 24 |
| [3, 2, 2, 2, 2, 4, 3, 2, 2, 3, 2, 2, 2] | [3, 2, 2, 2, 2, 4, 2, 3, 2, 2, 3, 2, 2, 2] | [3, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 2] | 24 |
| [3, [2], [2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]] | [2, [2], [2], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]] | [2, [2], [2], [2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]] | 24 |
| [2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2] | [2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2] | [2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2] | 24 |
| [25, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [25, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [25, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [5, 6, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [5, 6, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [5, 6, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 7, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 7, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 7, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [4, 2, 5, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [4, 2, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [4, 2, 5, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 2, 4, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 4, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 4, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [3, 2, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 24 |
Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87