List of log del Pezzo surfaces of Picard number one with index 1

28 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups
Local indices Index Cascade
\(\phi\) 9 1 - 1 cascade
[2] 8 2 1 1 cascade
[2], [2, 2] 6 2, 3 1, 1 1 cascade
[2, 2, 2, 2] 5 5 1 1 cascade
[2], [2], [2, 2, 2] 4 2, 2, 4 1, 1, 1 1 cascade
[2, [2], [2], [2, 2]] 4 12 1 1 cascade
[2], [2, 2, 2, 2, 2] 3 2, 6 1, 1 1 cascade
[2, 2], [2, 2], [2, 2] 3 3, 3, 3 1, 1, 1 1 cascade
[2, [2], [2, 2], [2, 2]] 3 24 1 1 cascade
[2], [2, 2, 2], [2, 2, 2] 2 2, 4, 4 1, 1, 1 1 cascade
[2, 2], [2, 2, 2, 2, 2] 2 3, 6 1, 1 1 cascade
[2, 2, 2, 2, 2, 2, 2] 2 8 1 1 cascade
[2], [2], [2], [2, [2], [2], [2]] 2 2, 2, 2, 8 1, 1, 1, 1 1 cascade
[2], [2, [2], [2], [2, 2, 2]] 2 2, 16 1, 1 1 cascade
[2, [2], [2, 2], [2, 2, 2]] 2 48 1 1 cascade
[2], [2], [2, 2, 2], [2, 2, 2] 1 2, 2, 4, 4 1, 1, 1, 1 1 cascade
[2], [2, 2], [2, 2, 2, 2, 2] 1 2, 3, 6 1, 1, 1 1 cascade
[2], [2, 2, 2, 2, 2, 2, 2] 1 2, 8 1, 1 1 cascade
[2, 2], [2, 2], [2, 2], [2, 2] 1 3, 3, 3, 3 1, 1, 1, 1 1 cascade
[2, 2, 2, 2], [2, 2, 2, 2] 1 5, 5 1, 1 1 cascade
[2, 2, 2, 2, 2, 2, 2, 2] 1 9 1 1 cascade
[2], [2], [2, [2], [2], [2, 2, 2]] 1 2, 2, 16 1, 1, 1 1 cascade
[2], [2, [2], [2, 2], [2, 2, 2]] 1 2, 48 1, 1 1 cascade
[2, 2], [2, [2], [2, 2], [2, 2]] 1 3, 24 1, 1 1 cascade
[2, 2, 2], [2, [2], [2], [2, 2]] 1 4, 12 1, 1 1 cascade
[2, [2], [2], [2, 2, 2, 2, 2]] 1 24 1 1 cascade
[2, [2], [2, 2], [2, 2, 2, 2]] 1 120 1 1 cascade
[2, [2], [2], [2]], [2, [2], [2], [2]] 1 8, 8 1, 1 1 cascade