List of toric log del Pezzo surfaces of Picard number one with index 5

33 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups
Local indices Index Cascade
[5] 49/5 5 5 5 cascade
[10] 72/5 10 5 5 cascade
[2], [2, 3] 32/5 2, 5 1, 5 5 cascade
[2], [2, 8] 54/5 2, 15 1, 5 5 cascade
[2, 2], [2, 3] 27/5 3, 5 1, 5 5 cascade
[2, 2], [3, 7] 48/5 3, 20 1, 5 5 cascade
[2], [2], [2, 6, 2] 36/5 2, 2, 20 1, 1, 5 5 cascade
[2], [2, 2], [2, 5, 3] 6 2, 3, 25 1, 1, 5 5 cascade
[5], [2, 2, 2, 2, 2] 24/5 5, 6 5, 1 5 cascade
[2], [2, 2, 2], [2, 2, 4] 16/5 2, 4, 10 1, 1, 5 5 cascade
[2, 2], [2, 2], [3, 4, 3] 24/5 3, 3, 30 1, 1, 5 5 cascade
[2, 2], [2, 2, 2], [2, 3] 12/5 3, 4, 5 1, 1, 5 5 cascade
[2, 2, 2, 2, 2], [6, 6] 42/5 6, 35 1, 5 5 cascade
[2], [5], [2, 2, 2, 2, 2, 2] 14/5 2, 5, 7 1, 5, 1 5 cascade
[2, 2, 2, 2, 2, 2], [3, 7] 28/5 7, 20 1, 5 5 cascade
[2, 3], [2, 3], [2, 2, 2, 2] 9/5 5, 5, 5 5, 5, 1 5 cascade
[2], [2, 2, 2, 2, 2], [2, 4, 6] 24/5 2, 6, 40 1, 1, 5 5 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 8] 24/5 8, 15 1, 5 5 cascade
[2, 3], [2, 2, 2, 2], [2, 2, 4] 8/5 5, 5, 10 5, 1, 5 5 cascade
[2, 2], [2, 2, 2, 2, 2], [3, 3, 6] 18/5 3, 6, 45 1, 1, 5 5 cascade
[2, 3], [2, 2, 4], [2, 2, 3, 2, 2] 6/5 5, 10, 15 5, 5, 5 5 cascade
[5], [5], [2, 2, 2, 2, 2, 2, 2, 2, 2] 8/5 5, 5, 10 5, 5, 1 5 cascade
[10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 22/5 10, 11 5, 1 5 cascade
[2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [2, 8] 9/5 3, 9, 15 1, 1, 5 5 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [3, 7] 8/5 4, 8, 20 1, 1, 5 5 cascade
[2], [10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 12/5 2, 10, 12 1, 5, 1 5 cascade
[2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [6, 2, 6] 12/5 6, 6, 60 1, 1, 5 5 cascade
[2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 8] 6/5 5, 10, 15 5, 1, 5 5 cascade
[2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2], [6, 6] 7/5 7, 7, 35 1, 1, 5 5 cascade
[2, 2, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 7] 4/5 10, 10, 20 5, 1, 5 5 cascade
[5], [10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 6/5 5, 10, 15 5, 5, 1 5 cascade
[2, 8], [2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 3/5 15, 15, 15 5, 5, 1 5 cascade
[10], [10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 4/5 10, 10, 20 5, 5, 1 5 cascade