List of toric log del Pezzo surfaces of Picard number one with index 8

27 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups
Local indices Index Cascade
[16] 81/4 16 8 8 cascade
[2, 2], [3, 11] 27/2 3, 32 1, 8 8 cascade
[2], [2], [2, 5, 2] 25/4 2, 2, 16 1, 1, 8 8 cascade
[2, 2], [2, 2], [3, 6, 3] 27/4 3, 3, 48 1, 1, 8 8 cascade
[4], [2, 2, 2], [2, 2, 2, 2, 4] 9/4 4, 4, 16 2, 1, 8 8 cascade
[2, 2, 2, 2, 2, 2, 2, 2], [9, 9] 45/4 9, 80 1, 8 8 cascade
[2, 2, 2], [2, 5, 2], [3, 2, 2, 2, 3] 5/4 4, 16, 20 1, 8, 2 8 cascade
[4], [3, 2, 3], [2, 2, 2, 2, 2, 4, 2] 3/2 4, 12, 32 2, 2, 8 8 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 11] 11/2 11, 32 1, 8 8 cascade
[2, 3, 2], [2, 5, 2], [3, 2, 2, 2, 2, 3] 3/4 8, 16, 24 4, 8, 2 8 cascade
[3, 3], [2, 2, 2, 2, 4], [2, 2, 4, 2, 2] 3/4 8, 16, 24 2, 8, 4 8 cascade
[2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 10] 15/4 2, 10, 48 1, 1, 8 8 cascade
[2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [3, 4, 9] 9/2 3, 9, 96 1, 1, 8 8 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 4], [5, 5] 3/4 8, 16, 24 1, 8, 4 8 cascade
[2, 2, 2, 2, 4], [2, 2, 2, 2, 4], [2, 2, 3, 5] 1/2 16, 16, 32 8, 8, 4 8 cascade
[2, 2, 6], [3, 2, 2, 3], [2, 2, 2, 2, 2, 4, 2] 1/2 16, 16, 32 4, 2, 8 8 cascade
[2, 5, 2], [2, 5, 2], [3, 2, 2, 2, 2, 2, 2, 3] 1/2 16, 16, 32 8, 8, 2 8 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 11] 3/2 4, 12, 32 1, 1, 8 8 cascade
[3, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 10] 3/4 12, 12, 48 2, 1, 8 8 cascade
[16], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 17/4 16, 17 8, 1 8 cascade
[2], [16], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 9/4 2, 16, 18 1, 8, 1 8 cascade
[2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [9, 2, 9] 9/4 9, 9, 144 1, 1, 8 8 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [9, 9] 5/4 10, 10, 80 1, 1, 8 8 cascade
[2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 11] 1/2 16, 16, 32 4, 1, 8 8 cascade
[4], [16], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 5/4 4, 16, 20 2, 8, 1 8 cascade
[8], [16], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 3/4 8, 16, 24 4, 8, 1 8 cascade
[16], [16], [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] 1/2 16, 16, 32 8, 8, 1 8 cascade