55 basic regular quotient singularity types and
80 irregular quotient singularity types
| Singularity type | Index |
|---|---|
| [44] | 22 |
| [9, 5] | 22 |
| [8, 3, 8] | 22 |
| [24, 2, 8] | 22 |
| [25, 2, 5] | 22 |
| [27, 2, 3] | 22 |
| [30, 2, 2] | 22 |
| [4, 2, 3, 3] | 22 |
| [5, 3, 4, 2] | 22 |
| [2, 2, 16, 2, 2] | 22 |
| [3, 2, 10, 2, 3] | 22 |
| [3, 2, 13, 2, 2] | 22 |
| [5, 2, 6, 2, 5] | 22 |
| [5, 2, 8, 2, 3] | 22 |
| [5, 2, 11, 2, 2] | 22 |
| [8, 2, 4, 2, 8] | 22 |
| [8, 2, 5, 2, 5] | 22 |
| [8, 2, 7, 2, 3] | 22 |
| [8, 2, 10, 2, 2] | 22 |
| [8, 3, 2, 4, 2] | 22 |
| [8, 5, 2, 2, 2] | 22 |
| [24, 2, 2, 4, 2] | 22 |
| [24, 4, 2, 2, 2] | 22 |
| [5, 3, 2, 2, 2, 4] | 22 |
| [2, 2, 2, 7, 2, 2, 2] | 22 |
| [2, 2, 10, 4, 2, 2, 2] | 22 |
| [2, 4, 2, 2, 10, 2, 2] | 22 |
| [2, 4, 2, 3, 2, 4, 2] | 22 |
| [2, 4, 2, 5, 2, 2, 2] | 22 |
| [2, 5, 2, 2, 2, 2, 2] | 22 |
| [3, 2, 7, 2, 2, 4, 2] | 22 |
| [3, 2, 7, 4, 2, 2, 2] | 22 |
| [5, 2, 5, 2, 2, 4, 2] | 22 |
| [5, 2, 5, 4, 2, 2, 2] | 22 |
| [8, 2, 4, 2, 2, 4, 2] | 22 |
| [8, 2, 4, 4, 2, 2, 2] | 22 |
| [8, 3, 2, 2, 2, 2, 4] | 22 |
| [24, 2, 2, 2, 2, 2, 4] | 22 |
| [26, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 2, 4, 4, 4, 2, 2, 2] | 22 |
| [2, 2, 12, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 4, 2, 2, 4, 2, 2, 4, 2] | 22 |
| [2, 4, 2, 2, 4, 4, 2, 2, 2] | 22 |
| [3, 2, 9, 2, 2, 2, 2, 2, 2] | 22 |
| [4, 2, 2, 2, 2, 2, 7, 2, 3] | 22 |
| [4, 2, 2, 2, 2, 2, 10, 2, 2] | 22 |
| [4, 2, 2, 2, 2, 3, 2, 4, 2] | 22 |
| [4, 2, 2, 2, 2, 5, 2, 2, 2] | 22 |
| [4, 2, 2, 3, 2, 2, 2, 2, 2] | 22 |
| [5, 2, 5, 2, 2, 2, 2, 2, 4] | 22 |
| [5, 2, 7, 2, 2, 2, 2, 2, 2] | 22 |
| [8, 2, 4, 2, 2, 2, 2, 2, 4] | 22 |
| [8, 2, 6, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 2, 4, 6, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 4, 2, 2, 6, 2, 2, 2, 2, 2, 2] | 22 |
| [4, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2] | 22 |
| [4, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2] | 22 |
| [4, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4] | 22 |
| [2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2] | 22 |
| [4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4] | 22 |
| [4, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [5, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [8, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [24, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [3, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [5, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [8, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [4, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [4, 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] | 22 |
| [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] | 22 |
| [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] | 22 |
| Basic singularity type | Second singularity type | Third singularity type | Index |
|---|---|---|---|
| [23, 23] | [23, 2, 23] | [23, 2, 2, 23] | 22 |
| [23, 3, 2, 8] | [23, 2, 3, 2, 8] | [23, 2, 2, 3, 2, 8] | 22 |
| [23, 4, 2, 5] | [23, 2, 4, 2, 5] | [23, 2, 2, 4, 2, 5] | 22 |
| [23, 6, 2, 3] | [23, 2, 6, 2, 3] | [23, 2, 2, 6, 2, 3] | 22 |
| [23, 9, 2, 2] | [23, 2, 9, 2, 2] | [23, 2, 2, 9, 2, 2] | 22 |
| [2, 2, 9, 9, 2, 2] | [2, 2, 9, 2, 9, 2, 2] | [2, 2, 9, 2, 2, 9, 2, 2] | 22 |
| [3, 2, 6, 6, 2, 3] | [3, 2, 6, 2, 6, 2, 3] | [3, 2, 6, 2, 2, 6, 2, 3] | 22 |
| [3, 2, 6, 9, 2, 2] | [3, 2, 6, 2, 9, 2, 2] | [3, 2, 6, 2, 2, 9, 2, 2] | 22 |
| [5, 2, 4, 4, 2, 5] | [5, 2, 4, 2, 4, 2, 5] | [5, 2, 4, 2, 2, 4, 2, 5] | 22 |
| [5, 2, 4, 6, 2, 3] | [5, 2, 4, 2, 6, 2, 3] | [5, 2, 4, 2, 2, 6, 2, 3] | 22 |
| [5, 2, 4, 9, 2, 2] | [5, 2, 4, 2, 9, 2, 2] | [5, 2, 4, 2, 2, 9, 2, 2] | 22 |
| [8, 2, 3, 3, 2, 8] | [8, 2, 3, 2, 3, 2, 8] | [8, 2, 3, 2, 2, 3, 2, 8] | 22 |
| [8, 2, 3, 4, 2, 5] | [8, 2, 3, 2, 4, 2, 5] | [8, 2, 3, 2, 2, 4, 2, 5] | 22 |
| [8, 2, 3, 6, 2, 3] | [8, 2, 3, 2, 6, 2, 3] | [8, 2, 3, 2, 2, 6, 2, 3] | 22 |
| [8, 2, 3, 9, 2, 2] | [8, 2, 3, 2, 9, 2, 2] | [8, 2, 3, 2, 2, 9, 2, 2] | 22 |
| [23, 3, 2, 2, 4, 2] | [23, 2, 3, 2, 2, 4, 2] | [23, 2, 2, 3, 2, 2, 4, 2] | 22 |
| [23, 3, 4, 2, 2, 2] | [23, 2, 3, 4, 2, 2, 2] | [23, 2, 2, 3, 4, 2, 2, 2] | 22 |
| [2, 2, 9, 3, 4, 2, 2, 2] | [2, 2, 9, 2, 3, 4, 2, 2, 2] | [2, 2, 9, 2, 2, 3, 4, 2, 2, 2] | 22 |
| [2, 4, 2, 2, 3, 9, 2, 2] | [2, 4, 2, 2, 3, 2, 9, 2, 2] | [2, 4, 2, 2, 3, 2, 2, 9, 2, 2] | 22 |
| [3, 2, 6, 3, 2, 2, 4, 2] | [3, 2, 6, 2, 3, 2, 2, 4, 2] | [3, 2, 6, 2, 2, 3, 2, 2, 4, 2] | 22 |
| [3, 2, 6, 3, 4, 2, 2, 2] | [3, 2, 6, 2, 3, 4, 2, 2, 2] | [3, 2, 6, 2, 2, 3, 4, 2, 2, 2] | 22 |
| [5, 2, 4, 3, 2, 2, 4, 2] | [5, 2, 4, 2, 3, 2, 2, 4, 2] | [5, 2, 4, 2, 2, 3, 2, 2, 4, 2] | 22 |
| [5, 2, 4, 3, 4, 2, 2, 2] | [5, 2, 4, 2, 3, 4, 2, 2, 2] | [5, 2, 4, 2, 2, 3, 4, 2, 2, 2] | 22 |
| [8, 2, 3, 3, 2, 2, 4, 2] | [8, 2, 3, 2, 3, 2, 2, 4, 2] | [8, 2, 3, 2, 2, 3, 2, 2, 4, 2] | 22 |
| [8, 2, 3, 3, 4, 2, 2, 2] | [8, 2, 3, 2, 3, 4, 2, 2, 2] | [8, 2, 3, 2, 2, 3, 4, 2, 2, 2] | 22 |
| [23, 3, 2, 2, 2, 2, 2, 4] | [23, 2, 3, 2, 2, 2, 2, 2, 4] | [23, 2, 2, 3, 2, 2, 2, 2, 2, 4] | 22 |
| [23, 5, 2, 2, 2, 2, 2, 2] | [23, 2, 5, 2, 2, 2, 2, 2, 2] | [23, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 2, 4, 3, 3, 4, 2, 2, 2] | [2, 2, 2, 4, 3, 2, 3, 4, 2, 2, 2] | [2, 2, 2, 4, 3, 2, 2, 3, 4, 2, 2, 2] | 22 |
| [2, 2, 9, 5, 2, 2, 2, 2, 2, 2] | [2, 2, 9, 2, 5, 2, 2, 2, 2, 2, 2] | [2, 2, 9, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 4, 2, 2, 3, 3, 2, 2, 4, 2] | [2, 4, 2, 2, 3, 2, 3, 2, 2, 4, 2] | [2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2] | 22 |
| [2, 4, 2, 2, 3, 3, 4, 2, 2, 2] | [2, 4, 2, 2, 3, 2, 3, 4, 2, 2, 2] | [2, 4, 2, 2, 3, 2, 2, 3, 4, 2, 2, 2] | 22 |
| [3, 2, 6, 5, 2, 2, 2, 2, 2, 2] | [3, 2, 6, 2, 5, 2, 2, 2, 2, 2, 2] | [3, 2, 6, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 22 |
| [4, 2, 2, 2, 2, 2, 3, 6, 2, 3] | [4, 2, 2, 2, 2, 2, 3, 2, 6, 2, 3] | [4, 2, 2, 2, 2, 2, 3, 2, 2, 6, 2, 3] | 22 |
| [4, 2, 2, 2, 2, 2, 3, 9, 2, 2] | [4, 2, 2, 2, 2, 2, 3, 2, 9, 2, 2] | [4, 2, 2, 2, 2, 2, 3, 2, 2, 9, 2, 2] | 22 |
| [5, 2, 4, 3, 2, 2, 2, 2, 2, 4] | [5, 2, 4, 2, 3, 2, 2, 2, 2, 2, 4] | [5, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 4] | 22 |
| [5, 2, 4, 5, 2, 2, 2, 2, 2, 2] | [5, 2, 4, 2, 5, 2, 2, 2, 2, 2, 2] | [5, 2, 4, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 22 |
| [8, 2, 3, 3, 2, 2, 2, 2, 2, 4] | [8, 2, 3, 2, 3, 2, 2, 2, 2, 2, 4] | [8, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 4] | 22 |
| [8, 2, 3, 5, 2, 2, 2, 2, 2, 2] | [8, 2, 3, 2, 5, 2, 2, 2, 2, 2, 2] | [8, 2, 3, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 2, 4, 3, 5, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 4, 3, 2, 5, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 4, 3, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 4, 2, 2, 3, 5, 2, 2, 2, 2, 2, 2] | [2, 4, 2, 2, 3, 2, 5, 2, 2, 2, 2, 2, 2] | [2, 4, 2, 2, 3, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 22 |
| [4, 2, 2, 2, 2, 2, 3, 3, 2, 2, 4, 2] | [4, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 4, 2] | [4, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2] | 22 |
| [4, 2, 2, 2, 2, 2, 3, 3, 4, 2, 2, 2] | [4, 2, 2, 2, 2, 2, 3, 2, 3, 4, 2, 2, 2] | [4, 2, 2, 2, 2, 2, 3, 2, 2, 3, 4, 2, 2, 2] | 22 |
| [2, 2, 2, 2, 2, 2, 5, 5, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 5, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 22 |
| [4, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 4] | [4, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 4] | [4, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 4] | 22 |
| [4, 2, 2, 2, 2, 2, 3, 5, 2, 2, 2, 2, 2, 2] | [4, 2, 2, 2, 2, 2, 3, 2, 5, 2, 2, 2, 2, 2, 2] | [4, 2, 2, 2, 2, 2, 3, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 22 |
| [23, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [23, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [23, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 2, 9, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 9, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 9, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [3, 2, 6, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 6, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 6, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [5, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [5, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [5, 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] | 22 |
| [8, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [8, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [8, 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] | 22 |
| [2, 2, 2, 4, 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, 4, 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, 4, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
| [2, 4, 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, 4, 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, 4, 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] | 22 |
| [2, 2, 2, 2, 2, 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, 2, 2, 2, 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, 2, 2, 2, 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] | 22 |
| [4, 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] | [4, 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] | [4, 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] | 22 |
| [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, 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, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 22 |
Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87