40 basic regular quotient singularity types and
52 irregular quotient singularity types
| Singularity type | Index |
|---|---|
| [32] | 16 |
| [2, 9, 2] | 16 |
| [6, 3, 6] | 16 |
| [6, 6, 2] | 16 |
| [7, 2, 3] | 16 |
| [18, 2, 6] | 16 |
| [18, 5, 2] | 16 |
| [22, 2, 2] | 16 |
| [19, 2, 2, 3] | 16 |
| [2, 2, 12, 2, 2] | 16 |
| [2, 5, 4, 5, 2] | 16 |
| [2, 5, 8, 2, 2] | 16 |
| [4, 2, 2, 6, 2] | 16 |
| [4, 2, 3, 2, 3] | 16 |
| [4, 3, 2, 2, 2] | 16 |
| [6, 2, 4, 2, 6] | 16 |
| [6, 2, 4, 5, 2] | 16 |
| [6, 2, 8, 2, 2] | 16 |
| [6, 3, 2, 2, 4] | 16 |
| [18, 2, 2, 2, 4] | 16 |
| [20, 2, 2, 2, 2] | 16 |
| [3, 2, 2, 5, 5, 2] | 16 |
| [3, 2, 2, 9, 2, 2] | 16 |
| [6, 2, 5, 2, 2, 3] | 16 |
| [2, 2, 10, 2, 2, 2, 2] | 16 |
| [2, 5, 6, 2, 2, 2, 2] | 16 |
| [3, 2, 2, 6, 2, 2, 3] | 16 |
| [4, 2, 2, 2, 4, 5, 2] | 16 |
| [4, 2, 2, 2, 8, 2, 2] | 16 |
| [4, 2, 2, 3, 2, 2, 4] | 16 |
| [6, 2, 4, 2, 2, 2, 4] | 16 |
| [6, 2, 6, 2, 2, 2, 2] | 16 |
| [3, 2, 2, 7, 2, 2, 2, 2] | 16 |
| [4, 2, 2, 2, 5, 2, 2, 3] | 16 |
| [2, 2, 2, 2, 8, 2, 2, 2, 2] | 16 |
| [4, 2, 2, 2, 4, 2, 2, 2, 4] | 16 |
| [4, 2, 2, 2, 6, 2, 2, 2, 2] | 16 |
| [2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [6, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [18, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [2, 5, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [6, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [3, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [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] | 16 |
| [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] | 16 |
| Basic singularity type | Second singularity type | Third singularity type | Index |
|---|---|---|---|
| [17, 17] | [17, 2, 17] | [17, 2, 2, 17] | 16 |
| [2, [2], [2], [9]] | [2, [2], [2], [2, 9]] | [2, [2], [2], [2, 2, 9]] | 16 |
| [4, [2], [2], [3]] | [2, [2], [2], [4, 3]] | [2, [2], [2], [2, 4, 3]] | 16 |
| [17, 3, 2, 6] | [17, 2, 3, 2, 6] | [17, 2, 2, 3, 2, 6] | 16 |
| [17, 3, 5, 2] | [17, 2, 3, 5, 2] | [17, 2, 2, 3, 5, 2] | 16 |
| [17, 7, 2, 2] | [17, 2, 7, 2, 2] | [17, 2, 2, 7, 2, 2] | 16 |
| [3, [2], [2], [3, 2]] | [2, [2], [2], [3, 3, 2]] | [2, [2], [2], [2, 3, 3, 2]] | 16 |
| [17, 4, 2, 2, 3] | [17, 2, 4, 2, 2, 3] | [17, 2, 2, 4, 2, 2, 3] | 16 |
| [2, 2, 7, 7, 2, 2] | [2, 2, 7, 2, 7, 2, 2] | [2, 2, 7, 2, 2, 7, 2, 2] | 16 |
| [2, 5, 3, 3, 5, 2] | [2, 5, 3, 2, 3, 5, 2] | [2, 5, 3, 2, 2, 3, 5, 2] | 16 |
| [2, 5, 3, 7, 2, 2] | [2, 5, 3, 2, 7, 2, 2] | [2, 5, 3, 2, 2, 7, 2, 2] | 16 |
| [6, 2, 3, 3, 2, 6] | [6, 2, 3, 2, 3, 2, 6] | [6, 2, 3, 2, 2, 3, 2, 6] | 16 |
| [6, 2, 3, 3, 5, 2] | [6, 2, 3, 2, 3, 5, 2] | [6, 2, 3, 2, 2, 3, 5, 2] | 16 |
| [6, 2, 3, 7, 2, 2] | [6, 2, 3, 2, 7, 2, 2] | [6, 2, 3, 2, 2, 7, 2, 2] | 16 |
| [17, 3, 2, 2, 2, 4] | [17, 2, 3, 2, 2, 2, 4] | [17, 2, 2, 3, 2, 2, 2, 4] | 16 |
| [17, 5, 2, 2, 2, 2] | [17, 2, 5, 2, 2, 2, 2] | [17, 2, 2, 5, 2, 2, 2, 2] | 16 |
| [3, 2, 2, 4, 3, 5, 2] | [3, 2, 2, 4, 2, 3, 5, 2] | [3, 2, 2, 4, 2, 2, 3, 5, 2] | 16 |
| [3, 2, 2, 4, 7, 2, 2] | [3, 2, 2, 4, 2, 7, 2, 2] | [3, 2, 2, 4, 2, 2, 7, 2, 2] | 16 |
| [6, 2, 3, 4, 2, 2, 3] | [6, 2, 3, 2, 4, 2, 2, 3] | [6, 2, 3, 2, 2, 4, 2, 2, 3] | 16 |
| [2, 2, 7, 5, 2, 2, 2, 2] | [2, 2, 7, 2, 5, 2, 2, 2, 2] | [2, 2, 7, 2, 2, 5, 2, 2, 2, 2] | 16 |
| [2, 5, 3, 5, 2, 2, 2, 2] | [2, 5, 3, 2, 5, 2, 2, 2, 2] | [2, 5, 3, 2, 2, 5, 2, 2, 2, 2] | 16 |
| [3, 2, 2, 4, 4, 2, 2, 3] | [3, 2, 2, 4, 2, 4, 2, 2, 3] | [3, 2, 2, 4, 2, 2, 4, 2, 2, 3] | 16 |
| [4, 2, 2, 2, 3, 3, 5, 2] | [4, 2, 2, 2, 3, 2, 3, 5, 2] | [4, 2, 2, 2, 3, 2, 2, 3, 5, 2] | 16 |
| [4, 2, 2, 2, 3, 7, 2, 2] | [4, 2, 2, 2, 3, 2, 7, 2, 2] | [4, 2, 2, 2, 3, 2, 2, 7, 2, 2] | 16 |
| [6, 2, 3, 3, 2, 2, 2, 4] | [6, 2, 3, 2, 3, 2, 2, 2, 4] | [6, 2, 3, 2, 2, 3, 2, 2, 2, 4] | 16 |
| [6, 2, 3, 5, 2, 2, 2, 2] | [6, 2, 3, 2, 5, 2, 2, 2, 2] | [6, 2, 3, 2, 2, 5, 2, 2, 2, 2] | 16 |
| [3, 2, 2, 4, 5, 2, 2, 2, 2] | [3, 2, 2, 4, 2, 5, 2, 2, 2, 2] | [3, 2, 2, 4, 2, 2, 5, 2, 2, 2, 2] | 16 |
| [3, [2], [2], [2, 2, 2, 2, 2, 2]] | [2, [2], [2], [3, 2, 2, 2, 2, 2, 2]] | [2, [2], [2], [2, 3, 2, 2, 2, 2, 2, 2]] | 16 |
| [4, 2, 2, 2, 3, 4, 2, 2, 3] | [4, 2, 2, 2, 3, 2, 4, 2, 2, 3] | [4, 2, 2, 2, 3, 2, 2, 4, 2, 2, 3] | 16 |
| [2, 2, 2, 2, 5, 5, 2, 2, 2, 2] | [2, 2, 2, 2, 5, 2, 5, 2, 2, 2, 2] | [2, 2, 2, 2, 5, 2, 2, 5, 2, 2, 2, 2] | 16 |
| [4, 2, 2, 2, 3, 3, 2, 2, 2, 4] | [4, 2, 2, 2, 3, 2, 3, 2, 2, 2, 4] | [4, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 4] | 16 |
| [4, 2, 2, 2, 3, 5, 2, 2, 2, 2] | [4, 2, 2, 2, 3, 2, 5, 2, 2, 2, 2] | [4, 2, 2, 2, 3, 2, 2, 5, 2, 2, 2, 2] | 16 |
| [17, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [17, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [17, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [2, 2, 7, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 7, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 7, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [2, 5, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 5, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 5, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [6, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [6, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [6, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [3, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [2, 2, 2, 2, 5, 3, 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, 5, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [4, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [4, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [4, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
| [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, 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, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 16 |
Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87