List of toric log del Pezzo surfaces of Picard number one with index 14

74 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups		 Local indices Index Cascade
[28] 225/7 28 14 14 cascade
[2, 2], [3, 19] 150/7 3, 56 1, 14 14 cascade
[2, 2, 2, 2], [5, 17] 135/7 5, 84 1, 14 14 cascade
[2, 4], [3, 2, 2, 3] 36/7 7, 16 7, 2 14 cascade
[2], [4], [2, 2, 2, 3, 2] 25/7 2, 4, 14 1, 2, 7 14 cascade
[2, 2], [2, 2], [3, 10, 3] 75/7 3, 3, 84 1, 1, 14 14 cascade
[2], [3, 3], [2, 2, 2, 3, 2] 18/7 2, 8, 14 1, 2, 7 14 cascade
[3, 2, 2, 3], [2, 5, 2, 8] 68/7 16, 119 2, 7 14 cascade
[2], [2, 2, 2, 2, 2], [2, 3, 6] 27/7 2, 6, 28 1, 1, 14 14 cascade
[2, 2], [2, 2, 2, 2], [3, 8, 5] 60/7 3, 5, 112 1, 1, 14 14 cascade
[2, 2], [2, 4], [3, 2, 2, 2, 3] 15/7 3, 7, 20 1, 7, 2 14 cascade
[2, 2, 2, 2], [2, 2, 3], [3, 3] 10/7 5, 7, 8 1, 7, 2 14 cascade
[3, 2, 2, 2, 3], [2, 6, 2, 3] 5 20, 49 2, 7 14 cascade
[4], [4], [2, 2, 2, 5, 2, 2, 2] 32/7 4, 4, 56 2, 2, 14 14 cascade
[2], [3, 2, 2, 3], [2, 5, 2, 5, 2] 36/7 2, 16, 126 1, 2, 7 14 cascade
[3, 2, 2, 2, 2, 3], [2, 2, 7, 2] 30/7 24, 35 2, 7 14 cascade
[4], [2, 2, 2, 2], [2, 2, 2, 2, 5] 15/7 4, 5, 21 2, 1, 7 14 cascade
[4], [3, 3], [2, 2, 2, 4, 2, 3, 2] 24/7 4, 8, 84 2, 2, 14 14 cascade
[2, 2, 2, 2], [2, 2, 2, 2], [5, 6, 5] 45/7 5, 5, 140 1, 1, 14 14 cascade
[2, 4], [2, 4], [3, 2, 2, 2, 2, 2, 3] 9/7 7, 7, 28 7, 7, 2 14 cascade
[3, 3], [3, 3], [2, 3, 2, 3, 2, 3, 2] 16/7 8, 8, 112 2, 2, 14 14 cascade
[2, 2, 2], [3, 2, 2, 3], [2, 5, 2, 3, 4] 20/7 4, 16, 140 1, 2, 7 14 cascade
[2, 2, 3], [2, 2, 2, 2, 2, 2], [2, 3, 6] 9/7 7, 7, 28 7, 1, 14 14 cascade
[4], [7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 11/7 4, 7, 11 2, 7, 1 14 cascade
[2, 2, 2, 2, 2, 2, 2], [3, 2, 3], [2, 3, 6] 6/7 8, 12, 28 1, 2, 14 14 cascade
[2, 11], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3] 33/7 21, 44 7, 2 14 cascade
[4], [3, 2, 2, 2, 3], [2, 2, 2, 2, 2, 6, 2] 10/7 4, 20, 56 2, 2, 7 14 cascade
[7], [2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 4] 9/7 7, 7, 28 7, 7, 14 14 cascade
[2, 2, 2], [2, 8, 2], [3, 2, 2, 2, 2, 2, 2, 3] 8/7 4, 28, 32 1, 7, 2 14 cascade
[2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 3], [2, 6, 4] 6/7 6, 24, 42 1, 2, 7 14 cascade
[2, 2, 3], [3, 2, 2, 2, 2, 2, 3], [2, 2, 7, 2] 5/7 7, 28, 35 7, 2, 7 14 cascade
[2, 4], [2, 2, 2, 2, 5], [2, 2, 2, 5, 2, 2, 2] 6/7 7, 21, 56 7, 7, 14 14 cascade
[2, 4], [2, 3, 6], [2, 2, 2, 2, 3, 2, 2, 2, 2] 5/7 7, 28, 35 7, 14, 7 14 cascade
[2, 2, 2, 3, 2], [3, 2, 2, 2, 2, 2, 3], [2, 6, 4] 3/7 14, 28, 42 7, 2, 7 14 cascade
[2, 4], [2, 2, 2, 2, 2, 2, 2, 2, 4], [2, 2, 7, 2] 5/7 7, 28, 35 7, 14, 7 14 cascade
[3, 2, 2, 3], [3, 2, 2, 3], [2, 5, 2, 2, 2, 5, 2] 8/7 16, 16, 224 2, 2, 7 14 cascade
[3, 3, 3], [2, 2, 2, 2, 5], [2, 2, 2, 4, 2, 3, 2] 3/7 21, 21, 84 7, 7, 14 14 cascade
[2, 2], [2, 11], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3] 12/7 3, 21, 48 1, 7, 2 14 cascade
[2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 3], [2, 5, 2, 2, 8] 12/7 8, 16, 168 1, 2, 7 14 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [15, 15] 120/7 15, 224 1, 14 14 cascade
[3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 10] 6/7 8, 12, 28 2, 1, 7 14 cascade
[3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 4], [2, 2, 6, 2, 2] 3/7 14, 28, 42 7, 14, 7 14 cascade
[2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 4], [4, 9] 5/7 7, 28, 35 1, 14, 7 14 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 3], [2, 5, 8] 5/7 10, 20, 70 1, 2, 7 14 cascade
[2, 2, 2, 3, 2], [2, 2, 2, 2, 2, 2, 2, 2, 4], [3, 2, 9] 3/7 14, 28, 42 7, 14, 7 14 cascade
[2, 3, 6], [2, 2, 2, 2, 2, 2, 2, 2, 4], [2, 2, 5, 2, 3] 2/7 28, 28, 56 14, 14, 7 14 cascade
[2, 3, 6], [3, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 6, 2] 2/7 28, 28, 56 14, 2, 7 14 cascade
[7], [2, 2, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6] 6/7 7, 21, 56 7, 7, 14 14 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [5, 17] 51/7 17, 84 1, 14 14 cascade
[2, 4], [2, 11], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3] 6/7 7, 21, 56 7, 7, 2 14 cascade
[2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 6, 15] 45/7 3, 15, 252 1, 1, 14 14 cascade
[2, 2, 2, 2, 2, 2], [2, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6] 6/7 7, 21, 56 1, 7, 14 14 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 6], [3, 2, 9] 3/7 14, 28, 42 1, 14, 7 14 cascade
[4], [14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 9/7 4, 14, 18 2, 7, 1 14 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 19] 38/7 19, 56 1, 14 14 cascade
[2, 2, 10], [2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6] 2/7 28, 28, 56 7, 7, 14 14 cascade
[2, 8, 2], [2, 8, 2], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3] 2/7 28, 28, 56 7, 7, 2 14 cascade
[2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [5, 4, 15] 30/7 5, 15, 280 1, 1, 14 14 cascade
[4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 3, 16] 20/7 4, 16, 140 2, 1, 14 14 cascade
[3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 2, 2, 16] 12/7 8, 16, 168 2, 1, 14 14 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 19] 10/7 4, 20, 56 1, 1, 14 14 cascade
[2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [5, 17] 9/7 6, 18, 84 1, 1, 14 14 cascade
[2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 19] 6/7 7, 21, 56 7, 1, 14 14 cascade
[2, 11], [2, 11], [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3] 3/7 21, 21, 84 7, 7, 2 14 cascade
[2, 2, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [5, 17] 3/7 21, 21, 84 7, 1, 14 14 cascade
[28], [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] 29/7 28, 29 14, 1 14 cascade
[2], [28], [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] 15/7 2, 28, 30 1, 14, 1 14 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], [15, 2, 15] 15/7 15, 15, 420 1, 1, 14 14 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, 2, 2], [15, 15] 8/7 16, 16, 224 1, 1, 14 14 cascade
[2, 2, 10], [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, 19] 2/7 28, 28, 56 7, 1, 14 14 cascade
[4], [28], [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] 8/7 4, 28, 32 2, 14, 1 14 cascade
[7], [28], [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] 5/7 7, 28, 35 7, 14, 1 14 cascade
[14], [28], [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] 3/7 14, 28, 42 7, 14, 1 14 cascade
[28], [28], [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, 2, 2, 2, 2] 2/7 28, 28, 56 14, 14, 1 14 cascade