List of toric log del Pezzo surfaces of Picard number one with index 15

133 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups		 Local indices Index Cascade
[15] 289/15 15 15 15 cascade
[30] 512/15 30 15 15 cascade
[2], [2, 23] 128/5 2, 45 1, 15 15 cascade
[3], [2, 2, 4] 98/15 3, 10 3, 5 15 cascade
[2], [2], [2, 16, 2] 256/15 2, 2, 60 1, 1, 15 15 cascade
[2, 2, 2], [4, 19] 64/3 4, 75 1, 15 15 cascade
[2, 3], [2, 3, 4] 32/5 5, 18 5, 3 15 cascade
[2], [2, 2, 2], [2, 12, 4] 64/5 2, 4, 90 1, 1, 15 15 cascade
[2], [2, 3], [2, 3, 3, 2] 56/15 2, 5, 21 1, 5, 3 15 cascade
[2, 2, 4], [4, 2, 2, 4] 88/15 10, 33 5, 3 15 cascade
[2, 5], [2, 2, 2, 3, 6] 8 9, 50 3, 5 15 cascade
[3], [3], [2, 2, 3, 2, 2] 49/15 3, 3, 15 3, 3, 5 15 cascade
[2, 3, 3, 2], [3, 3, 3, 3] 77/15 21, 55 3, 5 15 cascade
[2, 3, 4], [3, 3, 2, 2, 6] 38/5 18, 95 3, 5 15 cascade
[2], [2, 2, 4], [2, 3, 2, 2, 4] 16/5 2, 10, 36 1, 5, 3 15 cascade
[2], [2, 5], [2, 2, 2, 3, 4, 2] 22/5 2, 9, 55 1, 3, 5 15 cascade
[2, 2, 2], [2, 2, 2], [4, 8, 4] 128/15 4, 4, 120 1, 1, 15 15 cascade
[2, 2, 2], [2, 3], [2, 3, 2, 4] 12/5 4, 5, 27 1, 5, 3 15 cascade
[2, 2, 2, 2, 2, 2, 2], [8, 17] 96/5 8, 135 1, 15 15 cascade
[2, 3], [2, 3], [2, 3, 2, 3, 2] 32/15 5, 5, 30 5, 5, 3 15 cascade
[2, 3, 2, 4], [2, 2, 2, 4, 3] 21/5 27, 35 3, 5 15 cascade
[2, 5, 3], [2, 3, 2, 2, 3, 2] 13/3 25, 39 5, 3 15 cascade
[3], [5], [2, 2, 2, 2, 2, 2, 2] 32/15 3, 5, 8 3, 5, 1 15 cascade
[2], [2, 3, 4], [2, 4, 2, 2, 3, 3] 4 2, 18, 100 1, 3, 5 15 cascade
[2, 2], [2, 2, 3, 2, 2], [2, 3, 4] 8/5 3, 15, 18 1, 5, 3 15 cascade
[2, 2], [2, 5], [2, 2, 2, 3, 3, 3] 16/5 3, 9, 60 1, 3, 5 15 cascade
[2, 2], [6], [2, 2, 2, 2, 2, 2, 3] 32/15 3, 6, 15 1, 3, 15 15 cascade
[2, 3], [2, 2, 2, 2], [3, 2, 2, 5] 32/15 5, 5, 30 5, 1, 15 15 cascade
[2, 3], [2, 2, 2, 2, 2, 2], [2, 5] 7/5 5, 7, 9 5, 1, 3 15 cascade
[3], [2, 5], [2, 2, 2, 2, 2, 2, 3] 9/5 3, 9, 15 3, 3, 15 15 cascade
[3], [6], [2, 2, 2, 2, 2, 4, 2, 2] 18/5 3, 6, 45 3, 3, 15 15 cascade
[3, 7], [2, 3, 2, 2, 2, 2, 2, 4] 28/5 20, 63 5, 3 15 cascade
[5], [2, 3], [2, 2, 2, 2, 2, 2, 3] 5/3 5, 5, 15 5, 5, 15 15 cascade
[2], [2, 2, 2, 2, 2, 2, 2], [2, 10, 8] 32/3 2, 8, 150 1, 1, 15 15 cascade
[2, 2], [2, 3, 4], [3, 3, 2, 2, 3, 3] 14/5 3, 18, 105 1, 3, 5 15 cascade
[2, 2, 2], [2, 2, 4], [4, 2, 2, 2, 4] 28/15 4, 10, 42 1, 5, 3 15 cascade
[2, 3], [2, 2, 4], [2, 3, 2, 2, 2, 4] 8/5 5, 10, 45 5, 5, 3 15 cascade
[3], [2, 2, 2, 2, 2, 2], [2, 2, 2, 7] 7/3 3, 7, 25 3, 1, 5 15 cascade
[3], [2, 3, 3, 2], [2, 2, 2, 3, 3, 3] 28/15 3, 21, 60 3, 3, 5 15 cascade
[3], [2, 3, 4], [2, 2, 3, 3, 3, 2, 2] 14/5 3, 18, 105 3, 3, 15 15 cascade
[2], [3, 7], [2, 3, 2, 2, 2, 2, 2, 3, 2] 44/15 2, 20, 66 1, 5, 3 15 cascade
[2, 2, 2, 2, 2], [2, 4, 2], [3, 2, 2, 5] 16/15 6, 12, 30 1, 3, 15 15 cascade
[2, 3], [2, 2, 2, 2, 2, 2, 3], [2, 6, 2] 16/15 5, 15, 20 5, 15, 5 15 cascade
[2, 3], [2, 3, 2, 3, 2], [2, 2, 2, 4, 3] 14/15 5, 30, 35 5, 3, 5 15 cascade
[2, 5], [2, 4, 2], [2, 2, 2, 2, 2, 2, 3] 4/5 9, 12, 15 3, 3, 15 15 cascade
[3], [4, 2, 4], [2, 2, 2, 2, 2, 4, 2, 2] 8/5 3, 24, 45 3, 3, 15 15 cascade
[5], [2, 2, 4], [2, 2, 2, 2, 2, 4, 2, 2] 8/5 5, 10, 45 5, 5, 15 15 cascade
[5], [6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 22/15 5, 6, 11 5, 3, 1 15 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [4, 6, 8] 32/5 4, 8, 180 1, 1, 15 15 cascade
[2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 3], [3, 7] 16/15 5, 15, 20 1, 15, 5 15 cascade
[2, 2, 2, 2], [2, 5, 3], [2, 3, 2, 2, 2, 4] 1 5, 25, 45 1, 5, 3 15 cascade
[2, 2, 2, 2], [3, 2, 2, 5], [2, 2, 2, 4, 3] 14/15 5, 30, 35 1, 15, 5 15 cascade
[2, 2, 2, 2, 2], [2, 5], [2, 2, 2, 3, 2, 6] 2 6, 9, 75 1, 3, 5 15 cascade
[2, 2, 2, 2, 2], [3, 4, 3], [2, 3, 2, 2, 4] 4/5 6, 30, 36 1, 5, 3 15 cascade
[2, 2, 4], [2, 2, 2, 2, 2, 2, 3], [2, 5, 3] 2/3 10, 15, 25 5, 15, 5 15 cascade
[2, 2, 4], [2, 2, 4], [4, 2, 2, 2, 2, 2, 4] 16/15 10, 10, 60 5, 5, 3 15 cascade
[2, 5], [2, 5], [2, 2, 2, 3, 2, 3, 2, 2, 2] 8/5 9, 9, 90 3, 3, 5 15 cascade
[3], [2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 3, 9] 16/5 3, 9, 60 3, 1, 15 15 cascade
[6], [2, 5], [2, 2, 2, 2, 2, 3, 2, 2, 2, 3] 2 6, 9, 75 3, 3, 15 15 cascade
[2, 2, 2], [3, 7], [2, 3, 2, 2, 2, 2, 2, 2, 4] 8/5 4, 20, 72 1, 5, 3 15 cascade
[2, 2, 2, 2, 2], [2, 3, 4], [3, 3, 2, 2, 2, 6] 8/5 6, 18, 120 1, 3, 5 15 cascade
[2, 2, 2, 2, 2, 2], [2, 3, 3, 2], [3, 3, 2, 6] 14/15 7, 21, 70 1, 3, 5 15 cascade
[2, 2, 3, 2, 2], [3, 4, 3], [2, 3, 2, 2, 2, 4] 2/5 15, 30, 45 5, 5, 3 15 cascade
[2, 2, 4], [2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 7] 2/3 10, 15, 25 5, 15, 5 15 cascade
[2, 2, 4], [3, 2, 2, 5], [2, 2, 2, 4, 2, 2, 2] 8/15 10, 30, 40 5, 15, 5 15 cascade
[2, 3], [2, 2, 2, 7], [2, 2, 2, 2, 2, 4, 2, 2] 1 5, 25, 45 5, 5, 15 15 cascade
[2, 3], [3, 7], [2, 2, 2, 2, 2, 3, 2, 2, 2, 3] 4/3 5, 20, 75 5, 5, 15 15 cascade
[2, 3], [3, 7], [2, 3, 2, 2, 2, 2, 2, 2, 3, 2] 4/3 5, 20, 75 5, 5, 3 15 cascade
[2, 3, 3, 2], [2, 3, 3, 2], [3, 3, 2, 2, 3, 3] 7/15 21, 21, 105 3, 3, 5 15 cascade
[2, 5], [2, 3, 2, 4], [2, 2, 2, 2, 2, 4, 2, 2] 3/5 9, 27, 45 3, 3, 15 15 cascade
[2, 5], [2, 3, 4], [2, 2, 2, 3, 2, 2, 2, 3, 3] 6/5 9, 18, 135 3, 3, 5 15 cascade
[2, 5], [2, 3, 4], [2, 2, 3, 3, 2, 2, 2, 2, 3] 6/5 9, 18, 135 3, 3, 15 15 cascade
[3], [10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 26/15 3, 10, 13 3, 5, 1 15 cascade
[4, 4], [2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 5, 2] 8/15 15, 15, 30 3, 15, 5 15 cascade
[5], [2, 6, 2], [2, 2, 2, 2, 2, 3, 2, 2, 2, 3] 4/3 5, 20, 75 5, 5, 15 15 cascade
[2, 2, 2, 2, 2, 2, 2, 2], [2, 3, 2, 4], [3, 3, 6] 3/5 9, 27, 45 1, 3, 5 15 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 4], [2, 2, 2, 7] 2/3 10, 15, 25 1, 3, 5 15 cascade
[2, 2, 2, 2, 2, 2, 3], [2, 3, 2, 3, 2], [3, 3, 6] 2/5 15, 30, 45 15, 3, 5 15 cascade
[2, 2, 2, 2, 2, 2, 3], [3, 2, 2, 5], [2, 4, 4, 2] 2/5 15, 30, 45 15, 15, 5 15 cascade
[2, 3, 4], [2, 3, 4], [3, 3, 2, 2, 2, 2, 2, 3, 3] 4/5 18, 18, 180 3, 3, 5 15 cascade
[2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 8] 4/5 9, 12, 15 3, 1, 5 15 cascade
[3, 2, 2, 5], [2, 3, 2, 3, 2], [2, 2, 2, 3, 3, 3] 4/15 30, 30, 60 15, 3, 5 15 cascade
[2, 2, 2, 2], [10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5] 8/5 5, 10, 45 1, 5, 15 15 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 5], [2, 4, 6] 8/15 10, 30, 40 1, 15, 5 15 cascade
[2, 2, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 3, 9] 16/15 10, 10, 60 5, 1, 15 15 cascade
[2, 2, 4], [3, 7], [2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 4] 4/5 10, 20, 90 5, 5, 3 15 cascade
[2, 5], [2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 2, 2, 2, 9] 8/5 9, 9, 90 3, 1, 15 15 cascade
[2, 5, 3], [2, 5, 3], [2, 3, 2, 2, 2, 2, 2, 2, 3, 2] 1/3 25, 25, 75 5, 5, 3 15 cascade
[5], [2, 2, 2, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5] 1 5, 25, 45 5, 5, 15 15 cascade
[15], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 64/15 15, 16 15, 1 15 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [8, 4, 8] 64/15 8, 8, 240 1, 1, 15 15 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [16, 16] 272/15 16, 255 1, 15 15 cascade
[2, 5, 3], [2, 2, 2, 7], [2, 2, 2, 2, 2, 3, 2, 2, 2, 3] 1/3 25, 25, 75 5, 5, 15 15 cascade
[3, 3, 6], [2, 3, 2, 2, 2, 4], [2, 2, 2, 2, 2, 4, 2, 2] 1/5 45, 45, 45 5, 3, 15 15 cascade
[6], [10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 16/15 6, 10, 16 3, 5, 1 15 cascade
[2], [15], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 34/15 2, 15, 17 1, 15, 1 15 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 6, 2], [3, 2, 2, 2, 2, 9] 4/5 10, 20, 90 1, 5, 15 15 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 2, 4], [2, 2, 3, 9] 8/15 12, 24, 60 1, 3, 15 15 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 17] 51/5 17, 135 1, 15 15 cascade
[2, 8], [2, 2, 2, 5, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5] 2/5 15, 30, 45 5, 5, 15 15 cascade
[2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 9, 16] 48/5 2, 16, 270 1, 1, 15 15 cascade
[3], [15], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 8/5 3, 15, 18 3, 15, 1 15 cascade
[3, 7], [3, 7], [2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2] 8/15 20, 20, 120 5, 5, 3 15 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 19] 19/3 19, 75 1, 15 15 cascade
[10], [3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2] 4/5 10, 20, 90 5, 5, 15 15 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 5, 16] 16/3 4, 16, 300 1, 1, 15 15 cascade
[5], [15], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 16/15 5, 15, 20 5, 15, 1 15 cascade
[6], [15], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 14/15 6, 15, 21 3, 15, 1 15 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 23] 23/5 23, 45 1, 15 15 cascade
[2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 19] 4/3 5, 20, 75 1, 1, 15 15 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [8, 3, 16] 16/5 8, 16, 360 1, 1, 15 15 cascade
[2, 3, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 3, 2, 17] 4/5 18, 18, 180 3, 1, 15 15 cascade
[6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 18] 8/5 6, 18, 120 3, 1, 15 15 cascade
[10], [15], [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 10, 15, 25 5, 15, 1 15 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, 23] 8/5 3, 24, 45 1, 1, 15 15 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], [8, 17] 6/5 9, 18, 135 1, 1, 15 15 cascade
[2, 3], [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, 23] 1 5, 25, 45 5, 1, 15 15 cascade
[3, 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, 18] 8/15 20, 20, 120 5, 1, 15 15 cascade
[2, 2, 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], [4, 19] 1/3 25, 25, 75 5, 1, 15 15 cascade
[2, 5], [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, 23] 3/5 9, 27, 45 3, 1, 15 15 cascade
[15], [15], [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] 8/15 15, 15, 30 15, 15, 1 15 cascade
[30], [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] 62/15 30, 31 15, 1 15 cascade
[2], [30], [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] 32/15 2, 30, 32 1, 15, 1 15 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], [16, 2, 16] 32/15 16, 16, 480 1, 1, 15 15 cascade
[2, 8], [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, 23] 2/5 15, 30, 45 5, 1, 15 15 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, 2, 2], [16, 16] 17/15 17, 17, 255 1, 1, 15 15 cascade
[3], [30], [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] 22/15 3, 30, 33 3, 15, 1 15 cascade
[5], [30], [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] 14/15 5, 30, 35 5, 15, 1 15 cascade
[6], [30], [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] 4/5 6, 30, 36 3, 15, 1 15 cascade
[10], [30], [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] 8/15 10, 30, 40 5, 15, 1 15 cascade
[15], [30], [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] 2/5 15, 30, 45 15, 15, 1 15 cascade
[2, 23], [2, 23], [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] 1/5 45, 45, 45 15, 15, 1 15 cascade
[30], [30], [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, 2, 2, 2] 4/15 30, 30, 60 15, 15, 1 15 cascade