List of toric log del Pezzo surfaces of Picard number one with index 13

69 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups		 Local indices Index Cascade
[13] 225/13 13 13 13 cascade
[26] 392/13 26 13 13 cascade
[2], [2, 7] 128/13 2, 13 1, 13 13 cascade
[2], [2, 20] 294/13 2, 39 1, 13 13 cascade
[2, 2], [3, 9] 150/13 3, 26 1, 13 13 cascade
[2], [2], [2, 14, 2] 196/13 2, 2, 52 1, 1, 13 13 cascade
[2], [2, 2], [2, 3, 3] 54/13 2, 3, 13 1, 1, 13 13 cascade
[2, 2, 2, 2], [5, 8] 135/13 5, 39 1, 13 13 cascade
[2], [2, 2, 2], [2, 4, 4] 64/13 2, 4, 26 1, 1, 13 13 cascade
[2, 2], [2, 2], [3, 5, 3] 75/13 3, 3, 39 1, 1, 13 13 cascade
[2], [2, 2, 2, 2], [2, 2, 5] 40/13 2, 5, 13 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 2], [2, 7] 63/13 7, 13 1, 13 13 cascade
[2, 2, 2, 2, 2, 2], [7, 15] 224/13 7, 104 1, 13 13 cascade
[2, 2], [2, 2, 2, 2], [3, 4, 5] 60/13 3, 5, 52 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 2, 2], [5, 8] 96/13 8, 39 1, 13 13 cascade
[2], [2, 2, 2, 2, 2, 2], [2, 9, 7] 126/13 2, 7, 117 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 2, 2, 2], [3, 9] 72/13 9, 26 1, 13 13 cascade
[2, 2], [2, 2, 2, 2, 2, 2, 2], [2, 7] 24/13 3, 8, 13 1, 1, 13 13 cascade
[2, 2, 2, 2], [2, 2, 2, 2], [5, 3, 5] 45/13 5, 5, 65 1, 1, 13 13 cascade
[2, 2, 2, 4], [2, 2, 2, 4], [2, 2, 2, 4] 9/13 13, 13, 13 13, 13, 13 13 cascade
[2, 2, 5], [2, 3, 3], [2, 2, 2, 2, 2, 3] 9/13 13, 13, 13 13, 13, 13 13 cascade
[2, 3, 3], [2, 2, 2, 4], [2, 2, 3, 2, 3] 8/13 13, 13, 26 13, 13, 13 13 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [4, 2, 8] 32/13 4, 8, 52 1, 1, 13 13 cascade
[2, 2, 2, 4], [2, 2, 2, 2, 2, 3], [2, 4, 4] 8/13 13, 13, 26 13, 13, 13 13 cascade
[2, 3, 3], [2, 2, 3, 2, 3], [2, 4, 2, 2, 3] 6/13 13, 26, 39 13, 13, 13 13 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 9] 20/13 4, 10, 26 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 3], [2, 4, 4], [2, 4, 2, 2, 3] 6/13 13, 26, 39 13, 13, 13 13 cascade
[2, 2, 5], [2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 6] 8/13 13, 13, 26 13, 13, 13 13 cascade
[2, 2, 5], [2, 2, 3, 2, 3], [2, 2, 2, 2, 3, 4] 6/13 13, 26, 39 13, 13, 13 13 cascade
[2, 7], [2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 3, 2] 8/13 13, 13, 26 13, 13, 13 13 cascade
[13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 56/13 13, 14 13, 1 13 cascade
[2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [5, 8] 18/13 6, 9, 39 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2], [7, 4, 7] 56/13 7, 7, 182 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [14, 14] 210/13 14, 195 1, 13 13 cascade
[2, 2, 2, 4], [2, 2, 2, 2, 6], [2, 2, 2, 2, 3, 4] 6/13 13, 26, 39 13, 13, 13 13 cascade
[2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 3, 2], [3, 5, 3] 6/13 13, 26, 39 13, 13, 13 13 cascade
[2, 4, 2, 2, 3], [2, 4, 2, 2, 3], [2, 4, 2, 2, 3] 3/13 39, 39, 39 13, 13, 13 13 cascade
[2], [13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 30/13 2, 13, 15 1, 13, 1 13 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [7, 15] 120/13 15, 104 1, 13 13 cascade
[2, 4, 4], [2, 2, 2, 2, 6], [2, 2, 2, 2, 3, 2, 2, 3] 4/13 26, 26, 52 13, 13, 13 13 cascade
[2, 7], [2, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2] 6/13 13, 26, 39 13, 13, 13 13 cascade
[2, 7], [2, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 9/13 13, 13, 13 13, 13, 1 13 cascade
[2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 8, 14] 112/13 2, 14, 208 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 3, 2], [5, 8] 6/13 13, 26, 39 13, 13, 13 13 cascade
[2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 3, 2], [3, 4, 5] 4/13 26, 26, 52 13, 13, 13 13 cascade
[2, 2, 2, 4], [3, 9], [2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2] 6/13 13, 26, 39 13, 13, 13 13 cascade
[2, 2, 3, 2, 3], [2, 2, 2, 2, 2, 2, 2, 3, 2], [4, 2, 8] 4/13 26, 26, 52 13, 13, 13 13 cascade
[2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 9] 8/13 13, 13, 26 13, 1, 13 13 cascade
[3, 9], [2, 2, 3, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2] 4/13 26, 26, 52 13, 13, 13 13 cascade
[2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 16] 48/13 2, 16, 78 1, 1, 13 13 cascade
[2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 3, 15] 45/13 3, 15, 117 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 6], [5, 8] 6/13 13, 26, 39 1, 13, 13 13 cascade
[5, 8], [2, 2, 2, 2, 3, 4], [2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2] 3/13 39, 39, 39 13, 13, 13 13 cascade
[2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 18] 36/13 2, 18, 52 1, 1, 13 13 cascade
[2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [5, 2, 15] 30/13 5, 15, 130 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 20] 60/13 20, 39 1, 13 13 cascade
[2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [7, 3, 14] 42/13 7, 14, 273 1, 1, 13 13 cascade
[2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 20] 21/13 3, 21, 39 1, 1, 13 13 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [7, 15] 16/13 8, 16, 104 1, 1, 13 13 cascade
[13], [13], [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] 8/13 13, 13, 26 13, 13, 1 13 cascade
[26], [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] 54/13 26, 27 13, 1 13 cascade
[2], [26], [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] 28/13 2, 26, 28 1, 13, 1 13 cascade
[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], [14, 2, 14] 28/13 14, 14, 364 1, 1, 13 13 cascade
[2, 7], [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, 20] 6/13 13, 26, 39 13, 1, 13 13 cascade
[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], [14, 14] 15/13 15, 15, 195 1, 1, 13 13 cascade
[3, 9], [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, 18] 4/13 26, 26, 52 13, 1, 13 13 cascade
[13], [26], [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] 6/13 13, 26, 39 13, 13, 1 13 cascade
[2, 20], [2, 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] 3/13 39, 39, 39 13, 13, 1 13 cascade
[26], [26], [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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 4/13 26, 26, 52 13, 13, 1 13 cascade