List of toric log del Pezzo surfaces of Picard number one with index 10

51 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups		 Local indices Index Cascade
[20] 121/5 20 10 10 cascade
[2, 3], [3, 2, 3] 27/5 5, 12 5, 2 10 cascade
[4], [2, 2, 2, 7] 9 4, 25 2, 5 10 cascade
[2], [4], [2, 2, 2, 5, 2] 27/5 2, 4, 30 1, 2, 5 10 cascade
[3, 2, 3], [2, 4, 2, 6] 39/5 12, 65 2, 5 10 cascade
[2, 2], [2, 3], [3, 2, 2, 3] 12/5 3, 5, 16 1, 5, 2 10 cascade
[2, 2], [4], [2, 2, 2, 4, 3] 21/5 3, 4, 35 1, 2, 5 10 cascade
[2], [3, 2, 3], [2, 4, 2, 4, 2] 21/5 2, 12, 70 1, 2, 5 10 cascade
[2, 2, 2], [2, 2, 2], [4, 3, 4] 18/5 4, 4, 40 1, 1, 10 10 cascade
[2, 3], [2, 3], [3, 2, 2, 2, 3] 9/5 5, 5, 20 5, 5, 2 10 cascade
[4], [4], [2, 2, 2, 4, 2, 2, 2] 18/5 4, 4, 40 2, 2, 5 10 cascade
[2], [3, 2, 2, 3], [2, 2, 2, 5, 2] 12/5 2, 16, 30 1, 2, 5 10 cascade
[2, 2], [3, 2, 3], [2, 4, 2, 3, 3] 3 3, 12, 75 1, 2, 5 10 cascade
[2, 2, 2, 2, 2], [3, 3], [2, 2, 4] 6/5 6, 8, 10 1, 2, 5 10 cascade
[2, 8], [3, 2, 2, 2, 2, 2, 2, 3] 24/5 15, 32 5, 2 10 cascade
[4], [3, 3], [2, 2, 2, 2, 2, 3, 2] 8/5 4, 8, 20 2, 2, 10 10 cascade
[4], [5], [2, 2, 2, 2, 2, 2, 2, 2] 9/5 4, 5, 9 2, 5, 1 10 cascade
[5], [2, 3], [2, 2, 2, 2, 2, 3, 2] 9/5 5, 5, 20 5, 5, 10 10 cascade
[4], [2, 2, 2, 2, 2], [2, 2, 2, 3, 6] 3 4, 6, 50 2, 1, 5 10 cascade
[4], [3, 2, 3], [2, 2, 2, 3, 2, 4, 2] 12/5 4, 12, 80 2, 2, 5 10 cascade
[2, 2, 2], [2, 6, 2], [3, 2, 2, 2, 2, 3] 6/5 4, 20, 24 1, 5, 2 10 cascade
[2, 2, 2, 2], [2, 2, 3, 2, 2], [4, 3, 4] 6/5 5, 15, 40 1, 5, 10 10 cascade
[2, 2, 2, 2], [3, 2, 2, 2, 3], [2, 5, 3] 1 5, 20, 25 1, 2, 5 10 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [11, 11] 66/5 11, 120 1, 10 10 cascade
[2, 3], [2, 2, 2, 2, 2, 3, 2], [2, 5, 3] 1 5, 20, 25 5, 10, 5 10 cascade
[2, 2], [2, 8], [3, 2, 2, 2, 2, 2, 2, 2, 3] 9/5 3, 15, 36 1, 5, 2 10 cascade
[2, 2, 2, 2, 2], [3, 2, 3], [2, 4, 2, 2, 6] 9/5 6, 12, 90 1, 2, 5 10 cascade
[2, 2, 4], [2, 2, 2, 2, 2, 3, 2], [3, 4, 3] 3/5 10, 20, 30 5, 10, 5 10 cascade
[2, 2, 4], [3, 2, 2, 2, 3], [2, 2, 2, 5, 2] 3/5 10, 20, 30 5, 2, 5 10 cascade
[2, 3], [2, 2, 2, 2, 2, 3, 2], [2, 2, 2, 7] 1 5, 20, 25 5, 10, 5 10 cascade
[3, 2, 3], [3, 2, 3], [2, 4, 2, 2, 2, 4, 2] 6/5 12, 12, 120 2, 2, 5 10 cascade
[2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 3], [2, 4, 6] 4/5 8, 16, 40 1, 2, 5 10 cascade
[2, 3], [2, 8], [3, 2, 2, 2, 2, 2, 2, 2, 2, 3] 6/5 5, 15, 40 5, 5, 2 10 cascade
[3, 2, 2, 2, 3], [2, 2, 2, 2, 2, 3, 2], [2, 4, 6] 2/5 20, 20, 40 2, 10, 5 10 cascade
[4], [10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 7/5 4, 10, 14 2, 5, 1 10 cascade
[2, 6, 2], [2, 6, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2, 3] 2/5 20, 20, 40 5, 5, 2 10 cascade
[2, 8], [2, 2, 3, 2, 2], [2, 2, 2, 2, 2, 2, 2, 3, 4] 3/5 15, 15, 60 5, 5, 10 10 cascade
[2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 14] 14/5 2, 14, 40 1, 1, 10 10 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 2, 12] 12/5 4, 12, 80 1, 1, 10 10 cascade
[2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 14] 6/5 5, 15, 40 5, 1, 10 10 cascade
[2, 8], [2, 8], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3] 3/5 15, 15, 60 5, 5, 2 10 cascade
[3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 14] 4/5 8, 16, 40 2, 1, 10 10 cascade
[20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 21/5 20, 21 10, 1 10 cascade
[2], [20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 11/5 2, 20, 22 1, 10, 1 10 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [11, 2, 11] 11/5 11, 11, 220 1, 1, 10 10 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [11, 11] 6/5 12, 12, 120 1, 1, 10 10 cascade
[3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 14] 2/5 20, 20, 40 5, 1, 10 10 cascade
[4], [20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 6/5 4, 20, 24 2, 10, 1 10 cascade
[5], [20], [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 5, 20, 25 5, 10, 1 10 cascade
[10], [20], [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] 3/5 10, 20, 30 5, 10, 1 10 cascade
[20], [20], [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, 2, 2, 2, 2, 2, 2, 2, 2] 2/5 20, 20, 40 10, 10, 1 10 cascade