27 basic regular quotient singularity types and
31 irregular quotient singularity types
| Singularity type | Index |
|---|---|
| [9] | 9 |
| [18] | 9 |
| [11, 5] | 9 |
| [14, 2] | 9 |
| [2, 10, 2] | 9 |
| [5, 4, 5] | 9 |
| [5, 7, 2] | 9 |
| [6, 2, 3] | 9 |
| [3, 2, 2, 2] | 9 |
| [3, 3, 2, 2] | 9 |
| [11, 2, 2, 3] | 9 |
| [12, 2, 2, 2] | 9 |
| [2, 8, 2, 2, 2] | 9 |
| [2, [2], [2, 2], [3]] | 9 |
| [3, 2, 2, 7, 2] | 9 |
| [3, 2, 3, 2, 3] | 9 |
| [5, 4, 2, 2, 3] | 9 |
| [5, 5, 2, 2, 2] | 9 |
| [2, 2, 2, 6, 2, 2, 2] | 9 |
| [3, 2, 2, 4, 2, 2, 3] | 9 |
| [3, 2, 2, 5, 2, 2, 2] | 9 |
| [6, 2, 2, 2, 2, 2, 2] | 9 |
| [2, 2, 3, 2, 2, 2, 2, 2] | 9 |
| [11, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [2, 7, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [3, 2, 3, 2, 2, 2, 2, 2, 2] | 9 |
| [5, 4, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [3, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2] | 9 |
| [2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2] | 9 |
| Basic singularity type | Second singularity type | Third singularity type | Index |
|---|---|---|---|
| [10, 10] | [10, 2, 10] | [10, 2, 2, 10] | 9 |
| [10, 3, 5] | [10, 2, 3, 5] | [10, 2, 2, 3, 5] | 9 |
| [10, 6, 2] | [10, 2, 6, 2] | [10, 2, 2, 6, 2] | 9 |
| [2, 6, 6, 2] | [2, 6, 2, 6, 2] | [2, 6, 2, 2, 6, 2] | 9 |
| [2, [2], [2], [10]] | [2, [2], [2], [2, 10]] | [2, [2], [2], [2, 2, 10]] | 9 |
| [3, [2], [2], [5]] | [2, [2], [2], [3, 5]] | [2, [2], [2], [2, 3, 5]] | 9 |
| [5, 3, 3, 5] | [5, 3, 2, 3, 5] | [5, 3, 2, 2, 3, 5] | 9 |
| [5, 3, 6, 2] | [5, 3, 2, 6, 2] | [5, 3, 2, 2, 6, 2] | 9 |
| [6, [2], [2], [2]] | [2, [2], [2], [6, 2]] | [2, [2], [2], [2, 6, 2]] | 9 |
| [10, 3, 2, 2, 3] | [10, 2, 3, 2, 2, 3] | [10, 2, 2, 3, 2, 2, 3] | 9 |
| [10, 4, 2, 2, 2] | [10, 2, 4, 2, 2, 2] | [10, 2, 2, 4, 2, 2, 2] | 9 |
| [2, 6, 4, 2, 2, 2] | [2, 6, 2, 4, 2, 2, 2] | [2, 6, 2, 2, 4, 2, 2, 2] | 9 |
| [3, 2, 2, 3, 6, 2] | [3, 2, 2, 3, 2, 6, 2] | [3, 2, 2, 3, 2, 2, 6, 2] | 9 |
| [3, [2], [2], [2, 2, 3]] | [2, [2], [2], [3, 2, 2, 3]] | [2, [2], [2], [2, 3, 2, 2, 3]] | 9 |
| [4, [2], [2], [2, 2, 2]] | [2, [2], [2], [4, 2, 2, 2]] | [2, [2], [2], [2, 4, 2, 2, 2]] | 9 |
| [5, 3, 3, 2, 2, 3] | [5, 3, 2, 3, 2, 2, 3] | [5, 3, 2, 2, 3, 2, 2, 3] | 9 |
| [5, 3, 4, 2, 2, 2] | [5, 3, 2, 4, 2, 2, 2] | [5, 3, 2, 2, 4, 2, 2, 2] | 9 |
| [2, 2, 2, 4, 4, 2, 2, 2] | [2, 2, 2, 4, 2, 4, 2, 2, 2] | [2, 2, 2, 4, 2, 2, 4, 2, 2, 2] | 9 |
| [3, 2, 2, 3, 3, 2, 2, 3] | [3, 2, 2, 3, 2, 3, 2, 2, 3] | [3, 2, 2, 3, 2, 2, 3, 2, 2, 3] | 9 |
| [3, 2, 2, 3, 4, 2, 2, 2] | [3, 2, 2, 3, 2, 4, 2, 2, 2] | [3, 2, 2, 3, 2, 2, 4, 2, 2, 2] | 9 |
| [10, 3, 2, 2, 2, 2, 2, 2, 2] | [10, 2, 3, 2, 2, 2, 2, 2, 2, 2] | [10, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [2, 6, 3, 2, 2, 2, 2, 2, 2, 2] | [2, 6, 2, 3, 2, 2, 2, 2, 2, 2, 2] | [2, 6, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [3, [2], [2], [2, 2, 2, 2, 2, 2, 2]] | [2, [2], [2], [3, 2, 2, 2, 2, 2, 2, 2]] | [2, [2], [2], [2, 3, 2, 2, 2, 2, 2, 2, 2]] | 9 |
| [5, 3, 3, 2, 2, 2, 2, 2, 2, 2] | [5, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2] | [5, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [3, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2] | 9 |
| [2, 2, 2, 2, 2, 2, 2, 3, 3, 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, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2] | 9 |
Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87