65 basic regular quotient singularity types and
83 irregular quotient singularity types
| Singularity type | Index |
|---|---|
| [11] | 11 |
| [22] | 11 |
| [4, 3] | 11 |
| [6, 2] | 11 |
| [13, 6] | 11 |
| [14, 4] | 11 |
| [15, 3] | 11 |
| [17, 2] | 11 |
| [2, 12, 2] | 11 |
| [3, 8, 3] | 11 |
| [3, 10, 2] | 11 |
| [4, 6, 4] | 11 |
| [4, 7, 3] | 11 |
| [4, 9, 2] | 11 |
| [5, 2, 3] | 11 |
| [6, 4, 6] | 11 |
| [6, 5, 4] | 11 |
| [6, 6, 3] | 11 |
| [6, 8, 2] | 11 |
| [7, 3, 2] | 11 |
| [8, 2, 2] | 11 |
| [2, 3, 2, 2] | 11 |
| [2, [2], [3], [4]] | 11 |
| [3, [2], [3], [3]] | 11 |
| [7, 2, 2, 3] | 11 |
| [13, 2, 3, 2] | 11 |
| [13, 3, 2, 2] | 11 |
| [2, 2, 5, 2, 2] | 11 |
| [2, 3, 3, 3, 2] | 11 |
| [2, 3, 4, 2, 2] | 11 |
| [2, 4, 2, 2, 2] | 11 |
| [2, 8, 2, 3, 2] | 11 |
| [2, 8, 3, 2, 2] | 11 |
| [3, 2, 2, 2, 2] | 11 |
| [3, 6, 2, 3, 2] | 11 |
| [3, 6, 3, 2, 2] | 11 |
| [4, 5, 2, 3, 2] | 11 |
| [4, 5, 3, 2, 2] | 11 |
| [6, 4, 2, 3, 2] | 11 |
| [6, 4, 3, 2, 2] | 11 |
| [13, 2, 2, 2, 3] | 11 |
| [14, 2, 2, 2, 2] | 11 |
| [2, 9, 2, 2, 2, 2] | 11 |
| [3, 2, 2, 2, 8, 2] | 11 |
| [3, 2, 2, 3, 3, 2] | 11 |
| [3, 2, 2, 4, 2, 2] | 11 |
| [3, 2, 3, 2, 2, 2] | 11 |
| [3, 6, 2, 2, 2, 3] | 11 |
| [3, 7, 2, 2, 2, 2] | 11 |
| [4, 5, 2, 2, 2, 3] | 11 |
| [4, 6, 2, 2, 2, 2] | 11 |
| [6, 4, 2, 2, 2, 3] | 11 |
| [6, 5, 2, 2, 2, 2] | 11 |
| [2, 2, 3, 4, 3, 2, 2] | 11 |
| [2, 3, 2, 4, 2, 3, 2] | 11 |
| [2, 3, 2, 4, 3, 2, 2] | 11 |
| [2, [2], [3], [2, 2, 2, 2]] | 11 |
| [3, 2, 2, 3, 2, 2, 3] | 11 |
| [4, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 3, 5, 2, 2, 2, 2] | 11 |
| [2, 3, 2, 5, 2, 2, 2, 2] | 11 |
| [3, 2, 2, 2, 4, 2, 3, 2] | 11 |
| [3, 2, 2, 2, 4, 3, 2, 2] | 11 |
| [5, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 2, 2, 6, 2, 2, 2, 2] | 11 |
| [3, 2, 2, 2, 4, 2, 2, 2, 3] | 11 |
| [3, 2, 2, 2, 5, 2, 2, 2, 2] | 11 |
| [7, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [13, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [3, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [4, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [6, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 3, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 3, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [3, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| Basic singularity type | Second singularity type | Third singularity type | Index |
|---|---|---|---|
| [12, 12] | [12, 2, 12] | [12, 2, 2, 12] | 11 |
| [12, 3, 6] | [12, 2, 3, 6] | [12, 2, 2, 3, 6] | 11 |
| [12, 4, 4] | [12, 2, 4, 4] | [12, 2, 2, 4, 4] | 11 |
| [12, 5, 3] | [12, 2, 5, 3] | [12, 2, 2, 5, 3] | 11 |
| [12, 7, 2] | [12, 2, 7, 2] | [12, 2, 2, 7, 2] | 11 |
| [2, 7, 7, 2] | [2, 7, 2, 7, 2] | [2, 7, 2, 2, 7, 2] | 11 |
| [2, [2], [2], [12]] | [2, [2], [2], [2, 12]] | [2, [2], [2], [2, 2, 12]] | 11 |
| [3, 5, 5, 3] | [3, 5, 2, 5, 3] | [3, 5, 2, 2, 5, 3] | 11 |
| [3, 5, 7, 2] | [3, 5, 2, 7, 2] | [3, 5, 2, 2, 7, 2] | 11 |
| [3, [2], [2], [6]] | [2, [2], [2], [3, 6]] | [2, [2], [2], [2, 3, 6]] | 11 |
| [4, 4, 4, 4] | [4, 4, 2, 4, 4] | [4, 4, 2, 2, 4, 4] | 11 |
| [4, 4, 5, 3] | [4, 4, 2, 5, 3] | [4, 4, 2, 2, 5, 3] | 11 |
| [4, 4, 7, 2] | [4, 4, 2, 7, 2] | [4, 4, 2, 2, 7, 2] | 11 |
| [4, [2], [2], [4]] | [2, [2], [2], [4, 4]] | [2, [2], [2], [2, 4, 4]] | 11 |
| [5, [2], [2], [3]] | [2, [2], [2], [5, 3]] | [2, [2], [2], [2, 5, 3]] | 11 |
| [6, 3, 3, 6] | [6, 3, 2, 3, 6] | [6, 3, 2, 2, 3, 6] | 11 |
| [6, 3, 4, 4] | [6, 3, 2, 4, 4] | [6, 3, 2, 2, 4, 4] | 11 |
| [6, 3, 5, 3] | [6, 3, 2, 5, 3] | [6, 3, 2, 2, 5, 3] | 11 |
| [6, 3, 7, 2] | [6, 3, 2, 7, 2] | [6, 3, 2, 2, 7, 2] | 11 |
| [7, [2], [2], [2]] | [2, [2], [2], [7, 2]] | [2, [2], [2], [2, 7, 2]] | 11 |
| [12, 3, 2, 3, 2] | [12, 2, 3, 2, 3, 2] | [12, 2, 2, 3, 2, 3, 2] | 11 |
| [12, 3, 3, 2, 2] | [12, 2, 3, 3, 2, 2] | [12, 2, 2, 3, 3, 2, 2] | 11 |
| [2, 7, 3, 2, 3, 2] | [2, 7, 2, 3, 2, 3, 2] | [2, 7, 2, 2, 3, 2, 3, 2] | 11 |
| [2, 7, 3, 3, 2, 2] | [2, 7, 2, 3, 3, 2, 2] | [2, 7, 2, 2, 3, 3, 2, 2] | 11 |
| [3, 5, 3, 2, 3, 2] | [3, 5, 2, 3, 2, 3, 2] | [3, 5, 2, 2, 3, 2, 3, 2] | 11 |
| [3, 5, 3, 3, 2, 2] | [3, 5, 2, 3, 3, 2, 2] | [3, 5, 2, 2, 3, 3, 2, 2] | 11 |
| [3, [2], [2], [2, 3, 2]] | [2, [2], [2], [3, 2, 3, 2]] | [2, [2], [2], [2, 3, 2, 3, 2]] | 11 |
| [3, [2], [2], [3, 2, 2]] | [2, [2], [2], [3, 3, 2, 2]] | [2, [2], [2], [2, 3, 3, 2, 2]] | 11 |
| [4, 4, 3, 2, 3, 2] | [4, 4, 2, 3, 2, 3, 2] | [4, 4, 2, 2, 3, 2, 3, 2] | 11 |
| [4, 4, 3, 3, 2, 2] | [4, 4, 2, 3, 3, 2, 2] | [4, 4, 2, 2, 3, 3, 2, 2] | 11 |
| [6, 3, 3, 2, 3, 2] | [6, 3, 2, 3, 2, 3, 2] | [6, 3, 2, 2, 3, 2, 3, 2] | 11 |
| [6, 3, 3, 3, 2, 2] | [6, 3, 2, 3, 3, 2, 2] | [6, 3, 2, 2, 3, 3, 2, 2] | 11 |
| [12, 3, 2, 2, 2, 3] | [12, 2, 3, 2, 2, 2, 3] | [12, 2, 2, 3, 2, 2, 2, 3] | 11 |
| [12, 4, 2, 2, 2, 2] | [12, 2, 4, 2, 2, 2, 2] | [12, 2, 2, 4, 2, 2, 2, 2] | 11 |
| [2, 7, 4, 2, 2, 2, 2] | [2, 7, 2, 4, 2, 2, 2, 2] | [2, 7, 2, 2, 4, 2, 2, 2, 2] | 11 |
| [3, 2, 2, 2, 3, 7, 2] | [3, 2, 2, 2, 3, 2, 7, 2] | [3, 2, 2, 2, 3, 2, 2, 7, 2] | 11 |
| [3, 5, 3, 2, 2, 2, 3] | [3, 5, 2, 3, 2, 2, 2, 3] | [3, 5, 2, 2, 3, 2, 2, 2, 3] | 11 |
| [3, 5, 4, 2, 2, 2, 2] | [3, 5, 2, 4, 2, 2, 2, 2] | [3, 5, 2, 2, 4, 2, 2, 2, 2] | 11 |
| [3, [2], [2], [2, 2, 2, 3]] | [2, [2], [2], [3, 2, 2, 2, 3]] | [2, [2], [2], [2, 3, 2, 2, 2, 3]] | 11 |
| [4, 4, 3, 2, 2, 2, 3] | [4, 4, 2, 3, 2, 2, 2, 3] | [4, 4, 2, 2, 3, 2, 2, 2, 3] | 11 |
| [4, 4, 4, 2, 2, 2, 2] | [4, 4, 2, 4, 2, 2, 2, 2] | [4, 4, 2, 2, 4, 2, 2, 2, 2] | 11 |
| [4, [2], [2], [2, 2, 2, 2]] | [2, [2], [2], [4, 2, 2, 2, 2]] | [2, [2], [2], [2, 4, 2, 2, 2, 2]] | 11 |
| [6, 3, 3, 2, 2, 2, 3] | [6, 3, 2, 3, 2, 2, 2, 3] | [6, 3, 2, 2, 3, 2, 2, 2, 3] | 11 |
| [6, 3, 4, 2, 2, 2, 2] | [6, 3, 2, 4, 2, 2, 2, 2] | [6, 3, 2, 2, 4, 2, 2, 2, 2] | 11 |
| [2, 2, 3, 3, 3, 3, 2, 2] | [2, 2, 3, 3, 2, 3, 3, 2, 2] | [2, 2, 3, 3, 2, 2, 3, 3, 2, 2] | 11 |
| [2, 3, 2, 3, 3, 2, 3, 2] | [2, 3, 2, 3, 2, 3, 2, 3, 2] | [2, 3, 2, 3, 2, 2, 3, 2, 3, 2] | 11 |
| [2, 3, 2, 3, 3, 3, 2, 2] | [2, 3, 2, 3, 2, 3, 3, 2, 2] | [2, 3, 2, 3, 2, 2, 3, 3, 2, 2] | 11 |
| [2, 2, 3, 3, 4, 2, 2, 2, 2] | [2, 2, 3, 3, 2, 4, 2, 2, 2, 2] | [2, 2, 3, 3, 2, 2, 4, 2, 2, 2, 2] | 11 |
| [2, 3, 2, 3, 4, 2, 2, 2, 2] | [2, 3, 2, 3, 2, 4, 2, 2, 2, 2] | [2, 3, 2, 3, 2, 2, 4, 2, 2, 2, 2] | 11 |
| [3, 2, 2, 2, 3, 3, 2, 3, 2] | [3, 2, 2, 2, 3, 2, 3, 2, 3, 2] | [3, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2] | 11 |
| [3, 2, 2, 2, 3, 3, 3, 2, 2] | [3, 2, 2, 2, 3, 2, 3, 3, 2, 2] | [3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2] | 11 |
| [2, 2, 2, 2, 4, 4, 2, 2, 2, 2] | [2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2] | [2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2] | 11 |
| [3, 2, 2, 2, 3, 3, 2, 2, 2, 3] | [3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3] | [3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3] | 11 |
| [3, 2, 2, 2, 3, 4, 2, 2, 2, 2] | [3, 2, 2, 2, 3, 2, 4, 2, 2, 2, 2] | [3, 2, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2] | 11 |
| [12, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [12, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [12, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 7, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 7, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [2, 7, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [3, 5, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 5, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [3, [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, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2]] | 11 |
| [4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [4, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [4, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [6, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [6, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [6, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 3, 3, 3, 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, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 3, 2, 3, 3, 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, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [2, 2, 2, 2, 4, 3, 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, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [3, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | [3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2] | 11 |
| [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, 3, 2, 3, 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] | 11 |
Reference: R. Blache, "Two aspects of log terminal surface singularities", Abh. Math. Sem. Univ. Hamburg 64 (1994), 59-87