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

168 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, 7] 9 25 5 5 cascade
[2], [2], [2, 6, 2] 36/5 2, 2, 20 1, 1, 5 5 cascade
[2, 2, 2, 3, 6] 8 50 5 5 cascade
[2, [2], [2], [2, 6]] 36/5 220 5 5 cascade
[2], [2, 2], [2, 5, 3] 6 2, 3, 25 1, 1, 5 5 cascade
[2], [2, 2, 2, 5, 2] 27/5 2, 30 1, 5 5 cascade
[2], [3, 3, 2, 2, 6] 38/5 2, 95 1, 5 5 cascade
[2, 2], [2, 4, 2, 6] 39/5 3, 65 1, 5 5 cascade
[5], [2, 2, 2, 2, 2] 24/5 5, 6 5, 1 5 cascade
[2, [2], [3], [2, 2, 2]] 18/5 240 5 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, 2] 22/5 2, 55 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, 4, 3] 21/5 3, 35 1, 5 5 cascade
[2, 2, 2, 2, 2], [6, 6] 42/5 6, 35 1, 5 5 cascade
[2, 2, 2, 4, 2, 2, 2] 18/5 40 5 5 cascade
[2, 4, 2, 2, 2, 3, 3] 5 125 5 5 cascade
[2], [2], [2], [4, [2], [2], [2]] 18/5 2, 2, 2, 40 1, 1, 1, 5 5 cascade
[2], [2, [2], [2], [2, 4, 2]] 18/5 2, 240 1, 5 5 cascade
[2], [2], [2, 4, 2, 2, 3, 3] 4 2, 2, 100 1, 1, 5 5 cascade
[2], [2, 2], [2, 2, 3, 2, 2] 8/5 2, 3, 15 1, 1, 5 5 cascade
[2], [2, 2], [2, 4, 2, 4, 2] 21/5 2, 3, 70 1, 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, 3, 3, 3] 16/5 3, 60 1, 5 5 cascade
[2, 2, 2, 2, 2, 2], [3, 7] 28/5 7, 20 1, 5 5 cascade
[2, 2, 2, 3, 3, 2, 2, 2] 13/5 65 5 5 cascade
[2, 3], [2, 2, 2, 2, 2, 2] 7/5 5, 7 5, 1 5 cascade
[2, 3], [2, 3], [2, 2, 2, 2] 9/5 5, 5, 5 5, 5, 1 5 cascade
[6, 2, 2, 2, 2, 2, 2, 6] 37/5 185 5 5 cascade
[2], [2], [2, 2], [3, [2], [2], [3]] 12/5 2, 2, 3, 60 1, 1, 1, 5 5 cascade
[2], [2], [2, [2], [3], [2, 2, 2]] 8/5 2, 2, 240 1, 1, 5 5 cascade
[2], [2], [3, [2], [2], [2, 2, 2]] 9/5 2, 2, 80 1, 1, 5 5 cascade
[2, 2], [2, [2], [2], [2, 3, 3]] 12/5 3, 260 1, 5 5 cascade
[2, [2], [2], [2, 3, 2, 2, 2]] 9/5 280 5 5 cascade
[2], [2, 2], [3, 3, 2, 2, 3, 3] 14/5 2, 3, 105 1, 1, 5 5 cascade
[2], [2, 2, 2], [2, 2, 2], [2, 3] 2/5 2, 4, 4, 5 1, 1, 1, 5 5 cascade
[2], [2, 2, 2], [2, 2, 2, 5, 2] 12/5 2, 4, 30 1, 1, 5 5 cascade
[2], [2, 2, 2, 2, 2], [2, 2, 4] 6/5 2, 6, 10 1, 1, 5 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, 3, 2, 2, 3, 3] 11/5 2, 110 1, 5 5 cascade
[2, 2], [2, 2], [2, 2, 3, 2, 2] 3/5 3, 3, 15 1, 1, 5 5 cascade
[2, 2], [2, 2], [2, 4, 2, 3, 3] 3 3, 3, 75 1, 1, 5 5 cascade
[2, 2], [2, 2, 2, 3, 2, 4, 2] 12/5 3, 80 1, 5 5 cascade
[2, 2], [2, 3], [2, 2, 2, 2, 2] 2/5 3, 5, 6 1, 5, 1 5 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 8] 24/5 8, 15 1, 5 5 cascade
[2, 2, 2, 3, 2, 3, 2, 2, 2] 8/5 90 5 5 cascade
[2, 3], [2, 2, 2, 2], [2, 2, 4] 8/5 5, 5, 10 5, 1, 5 5 cascade
[2, 3], [2, 2, 2, 2, 2, 2, 2] 2/5 5, 8 5, 1 5 cascade
[5], [2, 2, 2, 2, 2, 2, 2, 2] 9/5 5, 9 5, 1 5 cascade
[2], [2], [2, [2], [2], [3, 2, 2, 2]] 4/5 2, 2, 180 1, 1, 5 5 cascade
[2], [2, 2], [2, 2], [2, [2], [3], [3]] 6/5 2, 3, 3, 120 1, 1, 1, 5 5 cascade
[2], [2, 2], [2, [2], [3], [2, 2, 2]] 3/5 2, 3, 240 1, 1, 5 5 cascade
[2], [2, 3], [2, [2], [2], [2, 2, 2]] 2/5 2, 5, 16 1, 5, 1 5 cascade
[2, 2, 2], [3, [2], [2], [2, 2, 2]] 4/5 4, 80 1, 5 5 cascade
[2, 3], [2, [2], [2, 2], [2, 2, 2]] 2/5 5, 48 5, 1 5 cascade
[2, [2], [2], [2, 2, 3, 2, 2, 2]] 4/5 380 5 5 cascade
[2], [2, 2], [2, 2, 2, 4, 2, 2, 2] 3/5 2, 3, 40 1, 1, 5 5 cascade
[2], [2, 2, 2], [2, 2, 2, 3, 3, 3] 6/5 2, 4, 60 1, 1, 5 5 cascade
[2], [2, 2, 2, 3, 2, 2, 2, 3, 3] 6/5 2, 135 1, 5 5 cascade
[2], [2, 4, 2, 2, 2, 2, 2, 2, 6] 19/5 2, 190 1, 5 5 cascade
[2, 2], [2, 2, 2, 2, 2], [2, 2, 4] 1/5 3, 6, 10 1, 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, 2], [2, 2, 2, 3, 2, 2, 4, 2] 7/5 3, 105 1, 5 5 cascade
[2, 2, 2, 2, 2], [2, 2, 2, 3, 6] 3 6, 50 1, 5 5 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 2, 4] 1/5 8, 10 1, 5 5 cascade
[2, 3], [2, 2, 4], [2, 2, 3, 2, 2] 6/5 5, 10, 15 5, 5, 5 5 cascade
[2], [2], [2], [2, [2], [2], [2, 2, 3, 3]] 2/5 2, 2, 2, 360 1, 1, 1, 5 5 cascade
[2], [2], [2, 2], [2, [2], [2], [2, 4, 2]] 3/5 2, 2, 3, 240 1, 1, 1, 5 5 cascade
[2], [2], [5], [2, [2], [2], [2, 2, 2, 2]] 4/5 2, 2, 5, 20 1, 1, 5, 1 5 cascade
[2], [2, 2, 2], [2, [2], [2], [2, 3, 3]] 2/5 2, 4, 260 1, 1, 5 5 cascade
[2], [2, 2, 4], [2, [2], [2], [2, 2, 2]] 1/5 2, 10, 16 1, 5, 1 5 cascade
[2], [2, [2], [2], [2, 2, 2, 2, 3, 3]] 2/5 2, 560 1, 5 5 cascade
[2, 2], [2, 2, 2], [2, [2], [2], [4, 2]] 3/5 3, 4, 140 1, 1, 5 5 cascade
[2, 2], [2, [2], [2], [2, 2, 2, 4, 2]] 3/5 3, 440 1, 5 5 cascade
[2, 2, 2], [5], [2, [2], [2], [2, 2, 2]] 4/5 4, 5, 16 1, 5, 1 5 cascade
[2, 2, 4], [2, [2], [2, 2], [2, 2, 2]] 1/5 10, 48 5, 1 5 cascade
[2, 3], [2, 2, 2, 2], [2, [2], [3], [3]] 3/5 5, 5, 120 5, 1, 5 5 cascade
[2, 3], [2, 2, 2, 2], [3, [2], [2], [3]] 4/5 5, 5, 60 5, 1, 5 5 cascade
[5], [2, [2], [2], [2, 2, 2, 2, 2, 2]] 4/5 5, 28 5, 1 5 cascade
[2], [2, [2], [2], [2]], [2, [2], [2], [3, 3]] 2/5 2, 8, 160 1, 1, 5 5 cascade
[2], [2, [2], [2], [2, 2]], [3, [2], [2], [3]] 2/5 2, 12, 60 1, 1, 5 5 cascade
[2, 2], [2, [2], [2], [2]], [4, [2], [2], [2]] 3/5 3, 8, 40 1, 1, 5 5 cascade
[2, [2], [3], [3]], [2, [2], [2, 2], [2, 2]] 1/5 120, 24 5, 1 5 cascade
[5], [2, [2], [2], [2]], [2, [2], [2], [2, 2]] 4/5 5, 8, 12 5, 1, 1 5 cascade
[2], [2], [3, 3, 2, 2, 2, 2, 2, 3, 3] 4/5 2, 2, 180 1, 1, 5 5 cascade
[2], [2, 2], [2, 4, 2, 2, 2, 2, 3, 3] 1 2, 3, 150 1, 1, 5 5 cascade
[2], [2, 2, 2], [2, 2, 2, 3, 2, 4, 2] 2/5 2, 4, 80 1, 1, 5 5 cascade
[2], [2, 2, 2, 2, 2], [2, 2, 2, 5, 2] 2/5 2, 6, 30 1, 1, 5 5 cascade
[2], [2, 2, 2, 3, 2, 2, 2, 2, 3, 3] 1/5 2, 160 1, 5 5 cascade
[2, 2], [2, 2], [2, 4, 2, 2, 2, 4, 2] 6/5 3, 3, 120 1, 1, 5 5 cascade
[2, 2], [2, 2, 2], [2, 2, 2, 3, 3, 3] 1/5 3, 4, 60 1, 1, 5 5 cascade
[2, 2], [2, 2, 2, 3, 2, 2, 2, 3, 3] 1/5 3, 135 1, 5 5 cascade
[2, 2], [3, 3, 2, 2, 2, 2, 2, 2, 6] 13/5 3, 195 1, 5 5 cascade
[2, 2, 2], [2, 2, 2, 2, 2], [2, 6, 2] 6/5 4, 6, 20 1, 1, 5 5 cascade
[2, 2, 2], [2, 2, 2, 2, 2], [3, 4, 3] 4/5 4, 6, 30 1, 1, 5 5 cascade
[2, 2, 2, 2], [2, 2, 2, 2], [2, 5, 3] 1 5, 5, 25 1, 1, 5 5 cascade
[2, 2, 2, 2, 2], [2, 2, 2, 3, 2, 6] 2 6, 75 1, 5 5 cascade
[2, 2, 2, 2, 2, 2], [2, 2, 2, 4, 3] 1/5 7, 35 1, 5 5 cascade
[2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 6] 2 200 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], [6]] 6/5 2, 2, 6, 120 1, 1, 1, 5 5 cascade
[2, 2, 2, 2, 2], [2, [2], [2], [2, 2, 6]] 6/5 6, 320 1, 5 5 cascade
[2, 3], [2, 2, 3, 2, 2], [2, [2], [3], [3]] 1/5 5, 15, 120 5, 5, 5 5 cascade
[2, 3], [2, 2, 4], [2, [2], [3], [2, 2, 2]] 1/5 5, 10, 240 5, 5, 5 5 cascade
[2, 3], [2, 2, 4], [3, [2], [2], [2, 2, 2]] 2/5 5, 10, 80 5, 5, 5 5 cascade
[5], [2, 2, 2, 2], [2, [2], [3], [2, 2, 2]] 2/5 5, 5, 240 5, 1, 5 5 cascade
[2], [2, 2, 2, 2, 2], [3, 3, 2, 2, 2, 6] 8/5 2, 6, 120 1, 1, 5 5 cascade
[2], [2, 2, 2, 2, 2, 2], [2, 4, 2, 4, 2] 1/5 2, 7, 70 1, 1, 5 5 cascade
[2, 2], [2, 2, 2, 2, 2], [2, 4, 2, 2, 6] 9/5 3, 6, 90 1, 1, 5 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, 2, 2, 2], [2, 2, 3, 2, 2], [3, 4, 3] 2/5 5, 15, 30 1, 5, 5 5 cascade
[2, 2, 2, 2], [2, 2, 4], [2, 2, 2, 5, 2] 3/5 5, 10, 30 1, 5, 5 5 cascade
[2, 2, 2, 2, 2], [2, 4, 2, 2, 2, 4, 2] 1/5 6, 120 1, 5 5 cascade
[2, 2, 2, 2, 2, 2, 2, 2], [2, 4, 4, 2] 1/5 9, 45 1, 5 5 cascade
[2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 6] 1 225 5 5 cascade
[2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2] 1/5 245 5 5 cascade
[2], [2], [2, 6, 2], [2, [2], [2], [2, 2, 2, 2]] 1/5 2, 2, 20, 20 1, 1, 5, 1 5 cascade
[2], [2], [2, [2], [2], [2, 2, 2, 2, 2, 2, 6]] 1/5 2, 2, 720 1, 1, 5 5 cascade
[2, 2, 2], [2, 6, 2], [2, [2], [2], [2, 2, 2]] 1/5 4, 20, 16 1, 5, 1 5 cascade
[2, 2, 2], [2, [2], [2], [2, 2, 2, 2, 2, 6]] 1/5 4, 620 1, 5 5 cascade
[2, 6, 2], [2, [2], [2], [2, 2, 2, 2, 2, 2]] 1/5 20, 28 5, 1 5 cascade
[2, [2], [2], [2, 2, 2, 2, 2, 2, 2, 2, 6]] 1/5 920 5 5 cascade
[2, 2, 2, 2], [4, [2], [2], [2]], [4, [2], [2], [2]] 1/5 5, 40, 40 1, 5, 5 5 cascade
[2, 6, 2], [2, [2], [2], [2]], [2, [2], [2], [2, 2]] 1/5 20, 8, 12 5, 1, 1 5 cascade
[2, [2], [2], [2]], [2, [2], [2], [2, 2, 2, 2, 6]] 1/5 8, 520 1, 5 5 cascade
[2, [2], [2], [2, 2]], [2, [2], [2], [2, 2, 2, 6]] 1/5 12, 420 1, 5 5 cascade
[2, [2], [2], [2, 2, 2]], [2, [2], [2], [2, 2, 6]] 1/5 16, 320 1, 5 5 cascade
[2, [2], [2], [2, 2, 2, 2]], [2, [2], [2], [2, 6]] 1/5 20, 220 1, 5 5 cascade
[2, [2], [2], [6]], [2, [2], [2], [2, 2, 2, 2, 2]] 1/5 120, 24 5, 1 5 cascade
[2], [3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6] 3/5 2, 270 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], [3, 3, 6] 3/5 3, 9, 45 1, 1, 5 5 cascade
[2, 2], [2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 6] 4/5 3, 240 1, 5 5 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [2, 4, 6] 4/5 4, 8, 40 1, 1, 5 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, 2, 2, 2, 2, 2], [2, 4, 2, 2, 2, 2, 6] 4/5 7, 140 1, 5 5 cascade
[2, 2, 2, 2, 2, 2, 2], [3, 3, 2, 2, 2, 6] 3/5 8, 120 1, 5 5 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 8] 4/5 12, 15 1, 5 5 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [3, 7] 3/5 12, 20 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], [6, 2, 2, 2, 2, 2, 2, 2, 6] 7/5 6, 210 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
[10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 7/5 10, 14 5, 1 5 cascade
[2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [6, 2, 6] 2/5 2, 12, 60 1, 1, 5 5 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 6, 2], [2, 6, 2] 2/5 10, 20, 20 1, 5, 5 5 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [6, 2, 2, 2, 6] 2/5 11, 110 1, 5 5 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [6, 6] 2/5 14, 35 1, 5 5 cascade
[6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6] 2/5 360 5 5 cascade
[2], [2], [10], [2, [2], [2], [2, 2, 2, 2, 2, 2, 2, 2, 2]] 2/5 2, 2, 10, 40 1, 1, 5, 1 5 cascade
[2, 2, 2], [10], [2, [2], [2], [2, 2, 2, 2, 2, 2, 2, 2]] 2/5 4, 10, 36 1, 5, 1 5 cascade
[10], [2, [2], [2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]] 2/5 10, 48 5, 1 5 cascade
[10], [2, [2], [2], [2]], [2, [2], [2], [2, 2, 2, 2, 2, 2, 2]] 2/5 10, 8, 32 5, 1, 1 5 cascade
[10], [2, [2], [2], [2, 2]], [2, [2], [2], [2, 2, 2, 2, 2, 2]] 2/5 10, 12, 28 5, 1, 1 5 cascade
[10], [2, [2], [2], [2, 2, 2]], [2, [2], [2], [2, 2, 2, 2, 2]] 2/5 10, 16, 24 5, 1, 1 5 cascade
[10], [2, [2], [2], [2, 2, 2, 2]], [2, [2], [2], [2, 2, 2, 2]] 2/5 10, 20, 20 5, 1, 1 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