44 basic regular quotient singularity types and
52 irregular quotient singularity types
| Singularity type | Index |
|---|---|
| [15] | 15 |
| [30] | 15 |
| [17, 8] | 15 |
| [19, 4] | 15 |
| [23, 2] | 15 |
| [2, 16, 2] | 15 |
| [4, 8, 4] | 15 |
| [4, 12, 2] | 15 |
| [8, 4, 8] | 15 |
| [8, 6, 4] | 15 |
| [8, 10, 2] | 15 |
| [5, 2, 2, 3] | 15 |
| [9, 3, 2, 2] | 15 |
| [17, 2, 3, 2, 2] | 15 |
| [2, 10, 2, 3, 2, 2] | 15 |
| [4, 6, 2, 3, 2, 2] | 15 |
| [8, 4, 2, 3, 2, 2] | 15 |
| [9, 2, 2, 2, 2, 3] | 15 |
| [2, 2, 3, 3, 3, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 2, 2] | 15 |
| [17, 2, 2, 2, 2, 2, 3] | 15 |
| [18, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 4, 2, 2, 2, 2, 2] | 15 |
| [2, 11, 2, 2, 2, 2, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 2, 10, 2] | 15 |
| [4, 6, 2, 2, 2, 2, 2, 3] | 15 |
| [4, 7, 2, 2, 2, 2, 2, 2] | 15 |
| [8, 4, 2, 2, 2, 2, 2, 3] | 15 |
| [8, 5, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 3, 2, 4, 2, 3, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 3, 3, 2, 2] | 15 |
| [3, 2, 2, 2, 3, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 3, 2, 5, 2, 2, 2, 2, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 2, 4, 2, 3, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3] | 15 |
| [5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3] | 15 |
| [3, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2] | 15 |
| [9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [17, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [4, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [8, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 3, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [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] | 15 |
| [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] | 15 |
| Basic singularity type | Second singularity type | Third singularity type | Index |
|---|---|---|---|
| [16, 16] | [16, 2, 16] | [16, 2, 2, 16] | 15 |
| [16, 3, 8] | [16, 2, 3, 8] | [16, 2, 2, 3, 8] | 15 |
| [16, 5, 4] | [16, 2, 5, 4] | [16, 2, 2, 5, 4] | 15 |
| [16, 9, 2] | [16, 2, 9, 2] | [16, 2, 2, 9, 2] | 15 |
| [2, 9, 9, 2] | [2, 9, 2, 9, 2] | [2, 9, 2, 2, 9, 2] | 15 |
| [2, [2], [2], [16]] | [2, [2], [2], [2, 16]] | [2, [2], [2], [2, 2, 16]] | 15 |
| [3, [2], [2], [8]] | [2, [2], [2], [3, 8]] | [2, [2], [2], [2, 3, 8]] | 15 |
| [4, 5, 5, 4] | [4, 5, 2, 5, 4] | [4, 5, 2, 2, 5, 4] | 15 |
| [4, 5, 9, 2] | [4, 5, 2, 9, 2] | [4, 5, 2, 2, 9, 2] | 15 |
| [5, [2], [2], [4]] | [2, [2], [2], [5, 4]] | [2, [2], [2], [2, 5, 4]] | 15 |
| [8, 3, 3, 8] | [8, 3, 2, 3, 8] | [8, 3, 2, 2, 3, 8] | 15 |
| [8, 3, 5, 4] | [8, 3, 2, 5, 4] | [8, 3, 2, 2, 5, 4] | 15 |
| [8, 3, 9, 2] | [8, 3, 2, 9, 2] | [8, 3, 2, 2, 9, 2] | 15 |
| [9, [2], [2], [2]] | [2, [2], [2], [9, 2]] | [2, [2], [2], [2, 9, 2]] | 15 |
| [16, 3, 2, 3, 2, 2] | [16, 2, 3, 2, 3, 2, 2] | [16, 2, 2, 3, 2, 3, 2, 2] | 15 |
| [2, 9, 3, 2, 3, 2, 2] | [2, 9, 2, 3, 2, 3, 2, 2] | [2, 9, 2, 2, 3, 2, 3, 2, 2] | 15 |
| [3, [2], [2], [2, 3, 2, 2]] | [2, [2], [2], [3, 2, 3, 2, 2]] | [2, [2], [2], [2, 3, 2, 3, 2, 2]] | 15 |
| [4, 5, 3, 2, 3, 2, 2] | [4, 5, 2, 3, 2, 3, 2, 2] | [4, 5, 2, 2, 3, 2, 3, 2, 2] | 15 |
| [8, 3, 3, 2, 3, 2, 2] | [8, 3, 2, 3, 2, 3, 2, 2] | [8, 3, 2, 2, 3, 2, 3, 2, 2] | 15 |
| [16, 3, 2, 2, 2, 2, 2, 3] | [16, 2, 3, 2, 2, 2, 2, 2, 3] | [16, 2, 2, 3, 2, 2, 2, 2, 2, 3] | 15 |
| [16, 4, 2, 2, 2, 2, 2, 2] | [16, 2, 4, 2, 2, 2, 2, 2, 2] | [16, 2, 2, 4, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 9, 4, 2, 2, 2, 2, 2, 2] | [2, 9, 2, 4, 2, 2, 2, 2, 2, 2] | [2, 9, 2, 2, 4, 2, 2, 2, 2, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 2, 3, 9, 2] | [3, 2, 2, 2, 2, 2, 3, 2, 9, 2] | [3, 2, 2, 2, 2, 2, 3, 2, 2, 9, 2] | 15 |
| [3, [2], [2], [2, 2, 2, 2, 2, 3]] | [2, [2], [2], [3, 2, 2, 2, 2, 2, 3]] | [2, [2], [2], [2, 3, 2, 2, 2, 2, 2, 3]] | 15 |
| [4, 5, 3, 2, 2, 2, 2, 2, 3] | [4, 5, 2, 3, 2, 2, 2, 2, 2, 3] | [4, 5, 2, 2, 3, 2, 2, 2, 2, 2, 3] | 15 |
| [4, 5, 4, 2, 2, 2, 2, 2, 2] | [4, 5, 2, 4, 2, 2, 2, 2, 2, 2] | [4, 5, 2, 2, 4, 2, 2, 2, 2, 2, 2] | 15 |
| [4, [2], [2], [2, 2, 2, 2, 2, 2]] | [2, [2], [2], [4, 2, 2, 2, 2, 2, 2]] | [2, [2], [2], [2, 4, 2, 2, 2, 2, 2, 2]] | 15 |
| [8, 3, 3, 2, 2, 2, 2, 2, 3] | [8, 3, 2, 3, 2, 2, 2, 2, 2, 3] | [8, 3, 2, 2, 3, 2, 2, 2, 2, 2, 3] | 15 |
| [8, 3, 4, 2, 2, 2, 2, 2, 2] | [8, 3, 2, 4, 2, 2, 2, 2, 2, 2] | [8, 3, 2, 2, 4, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 3, 2, 3, 3, 2, 3, 2, 2] | [2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2] | [2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2] | 15 |
| [2, 2, 3, 2, 3, 4, 2, 2, 2, 2, 2, 2] | [2, 2, 3, 2, 3, 2, 4, 2, 2, 2, 2, 2, 2] | [2, 2, 3, 2, 3, 2, 2, 4, 2, 2, 2, 2, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2] | [3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2] | [3, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2] | 15 |
| [2, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 2] | [2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3] | [3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3] | [3, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 3] | 15 |
| [3, 2, 2, 2, 2, 2, 3, 4, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 2, 2, 3, 2, 4, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 2, 2] | 15 |
| [16, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [16, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [16, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 9, 3, 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, 9, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [3, [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, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]] | 15 |
| [4, 5, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [4, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [4, 5, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [8, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [8, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [8, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 3, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [2, 2, 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, 4, 2, 3, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [3, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
| [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, 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, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 15 |
Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87