40 basic regular quotient singularity types and
52 irregular quotient singularity types
| Singularity type | Index |
|---|---|
| [40] | 20 |
| [23, 7] | 20 |
| [27, 3] | 20 |
| [2, 11, 2] | 20 |
| [3, 14, 3] | 20 |
| [7, 6, 7] | 20 |
| [7, 10, 3] | 20 |
| [22, 6, 2] | 20 |
| [3, 9, 6, 2] | 20 |
| [7, 5, 6, 2] | 20 |
| [2, 6, 4, 6, 2] | 20 |
| [8, 2, 2, 3, 2] | 20 |
| [23, 2, 2, 2, 3] | 20 |
| [3, 10, 2, 2, 2, 3] | 20 |
| [7, 6, 2, 2, 2, 3] | 20 |
| [2, 7, 2, 2, 2, 3, 2] | 20 |
| [2, 8, 2, 2, 2, 2, 2] | 20 |
| [3, 2, 2, 2, 5, 6, 2] | 20 |
| [3, 2, 3, 2, 2, 2, 2] | 20 |
| [22, 2, 2, 2, 2, 3, 2] | 20 |
| [22, 3, 2, 2, 2, 2, 2] | 20 |
| [3, 2, 2, 3, 2, 2, 3, 2] | 20 |
| [3, 9, 2, 2, 2, 2, 3, 2] | 20 |
| [3, 9, 3, 2, 2, 2, 2, 2] | 20 |
| [7, 5, 2, 2, 2, 2, 3, 2] | 20 |
| [7, 5, 3, 2, 2, 2, 2, 2] | 20 |
| [2, 6, 4, 2, 2, 2, 2, 3, 2] | 20 |
| [2, 6, 4, 3, 2, 2, 2, 2, 2] | 20 |
| [3, 2, 2, 2, 6, 2, 2, 2, 3] | 20 |
| [2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2] | 20 |
| [2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2] | 20 |
| [2, 3, 2, 2, 2, 4, 2, 2, 2, 2, 2] | 20 |
| [3, 2, 2, 2, 5, 2, 2, 2, 2, 3, 2] | 20 |
| [3, 2, 2, 2, 5, 3, 2, 2, 2, 2, 2] | 20 |
| [2, 2, 2, 2, 2, 3, 4, 3, 2, 2, 2, 2, 2] | 20 |
| [2, 3, 2, 2, 2, 2, 4, 2, 2, 2, 2, 3, 2] | 20 |
| [2, 3, 2, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2] | 20 |
| [4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [22, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [3, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [7, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [2, 6, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [3, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [2, 2, 2, 2, 2, 3, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [2, 3, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [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] | 20 |
| [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] | 20 |
| Basic singularity type | Second singularity type | Third singularity type | Index |
|---|---|---|---|
| [21, 21] | [21, 2, 21] | [21, 2, 2, 21] | 20 |
| [21, 4, 7] | [21, 2, 4, 7] | [21, 2, 2, 4, 7] | 20 |
| [21, 8, 3] | [21, 2, 8, 3] | [21, 2, 2, 8, 3] | 20 |
| [2, [2], [2], [11]] | [2, [2], [2], [2, 11]] | [2, [2], [2], [2, 2, 11]] | 20 |
| [3, 8, 8, 3] | [3, 8, 2, 8, 3] | [3, 8, 2, 2, 8, 3] | 20 |
| [7, 4, 4, 7] | [7, 4, 2, 4, 7] | [7, 4, 2, 2, 4, 7] | 20 |
| [7, 4, 8, 3] | [7, 4, 2, 8, 3] | [7, 4, 2, 2, 8, 3] | 20 |
| [21, 3, 6, 2] | [21, 2, 3, 6, 2] | [21, 2, 2, 3, 6, 2] | 20 |
| [3, 8, 3, 6, 2] | [3, 8, 2, 3, 6, 2] | [3, 8, 2, 2, 3, 6, 2] | 20 |
| [3, [2], [2], [2, 4]] | [2, [2], [2], [3, 2, 4]] | [2, [2], [2], [2, 3, 2, 4]] | 20 |
| [5, [2], [2], [2, 2]] | [2, [2], [2], [5, 2, 2]] | [2, [2], [2], [2, 5, 2, 2]] | 20 |
| [7, 4, 3, 6, 2] | [7, 4, 2, 3, 6, 2] | [7, 4, 2, 2, 3, 6, 2] | 20 |
| [2, 6, 3, 3, 6, 2] | [2, 6, 3, 2, 3, 6, 2] | [2, 6, 3, 2, 2, 3, 6, 2] | 20 |
| [21, 4, 2, 2, 2, 3] | [21, 2, 4, 2, 2, 2, 3] | [21, 2, 2, 4, 2, 2, 2, 3] | 20 |
| [3, 8, 4, 2, 2, 2, 3] | [3, 8, 2, 4, 2, 2, 2, 3] | [3, 8, 2, 2, 4, 2, 2, 2, 3] | 20 |
| [7, 4, 4, 2, 2, 2, 3] | [7, 4, 2, 4, 2, 2, 2, 3] | [7, 4, 2, 2, 4, 2, 2, 2, 3] | 20 |
| [3, 2, 2, 2, 4, 3, 6, 2] | [3, 2, 2, 2, 4, 2, 3, 6, 2] | [3, 2, 2, 2, 4, 2, 2, 3, 6, 2] | 20 |
| [21, 3, 2, 2, 2, 2, 3, 2] | [21, 2, 3, 2, 2, 2, 2, 3, 2] | [21, 2, 2, 3, 2, 2, 2, 2, 3, 2] | 20 |
| [21, 3, 3, 2, 2, 2, 2, 2] | [21, 2, 3, 3, 2, 2, 2, 2, 2] | [21, 2, 2, 3, 3, 2, 2, 2, 2, 2] | 20 |
| [3, 8, 3, 2, 2, 2, 2, 3, 2] | [3, 8, 2, 3, 2, 2, 2, 2, 3, 2] | [3, 8, 2, 2, 3, 2, 2, 2, 2, 3, 2] | 20 |
| [3, 8, 3, 3, 2, 2, 2, 2, 2] | [3, 8, 2, 3, 3, 2, 2, 2, 2, 2] | [3, 8, 2, 2, 3, 3, 2, 2, 2, 2, 2] | 20 |
| [7, 4, 3, 2, 2, 2, 2, 3, 2] | [7, 4, 2, 3, 2, 2, 2, 2, 3, 2] | [7, 4, 2, 2, 3, 2, 2, 2, 2, 3, 2] | 20 |
| [7, 4, 3, 3, 2, 2, 2, 2, 2] | [7, 4, 2, 3, 3, 2, 2, 2, 2, 2] | [7, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2] | 20 |
| [2, 6, 3, 3, 2, 2, 2, 2, 3, 2] | [2, 6, 3, 2, 3, 2, 2, 2, 2, 3, 2] | [2, 6, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2] | 20 |
| [2, 6, 3, 3, 3, 2, 2, 2, 2, 2] | [2, 6, 3, 2, 3, 3, 2, 2, 2, 2, 2] | [2, 6, 3, 2, 2, 3, 3, 2, 2, 2, 2, 2] | 20 |
| [3, 2, 2, 2, 4, 4, 2, 2, 2, 3] | [3, 2, 2, 2, 4, 2, 4, 2, 2, 2, 3] | [3, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 3] | 20 |
| [3, [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, 3, 2, 2, 2, 2, 2, 2, 2, 2]] | 20 |
| [3, 2, 2, 2, 4, 3, 2, 2, 2, 2, 3, 2] | [3, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 3, 2] | [3, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 3, 2] | 20 |
| [3, 2, 2, 2, 4, 3, 3, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 4, 2, 3, 3, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2] | 20 |
| [2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 2, 2, 2] | 20 |
| [2, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 2] | [2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2] | [2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2] | 20 |
| [2, 3, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2] | [2, 3, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 2, 2, 2] | [2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 2, 2] | 20 |
| [21, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [21, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [21, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [3, 8, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 8, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 8, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [7, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [7, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [7, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [2, 6, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 6, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 6, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [3, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 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] | 20 |
| [2, 2, 2, 2, 2, 3, 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, 3, 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, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
| [2, 3, 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, 3, 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, 3, 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] | 20 |
| [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, 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, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 20 |
Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87