List of toric log del Pezzo surfaces of Picard number one with index 7

45 singularity types

Singularity types \(K^2\) Orders of local
fundamental groups
Local indices Index Cascade
[7] 81/7 7 7 7 cascade
[14] 128/7 14 7 7 cascade
[2], [2, 4] 50/7 2, 7 1, 7 7 cascade
[2], [2, 11] 96/7 2, 21 1, 7 7 cascade
[2, 2], [3, 5] 54/7 3, 14 1, 7 7 cascade
[2], [2], [2, 8, 2] 64/7 2, 2, 28 1, 1, 7 7 cascade
[2, 2, 2], [2, 4] 36/7 4, 7 1, 7 7 cascade
[2, 2, 2], [4, 9] 80/7 4, 35 1, 7 7 cascade
[2], [2, 2], [2, 2, 3] 24/7 2, 3, 7 1, 1, 7 7 cascade
[2, 2, 2, 2], [3, 5] 40/7 5, 14 1, 7 7 cascade
[2], [2, 2, 2], [2, 6, 4] 48/7 2, 4, 42 1, 1, 7 7 cascade
[2, 2], [2, 2], [3, 3, 3] 27/7 3, 3, 21 1, 1, 7 7 cascade
[2, 2], [2, 2, 2, 2], [2, 4] 15/7 3, 5, 7 1, 1, 7 7 cascade
[7], [2, 2, 2, 2, 2, 2, 2] 32/7 7, 8 7, 1 7 cascade
[2, 2, 2], [2, 2, 2], [4, 4, 4] 32/7 4, 4, 56 1, 1, 7 7 cascade
[2, 2, 2, 2, 2, 2, 2], [8, 8] 72/7 8, 63 1, 7 7 cascade
[2, 2, 3], [2, 2, 3], [2, 2, 3] 9/7 7, 7, 7 7, 7, 7 7 cascade
[2], [7], [2, 2, 2, 2, 2, 2, 2, 2] 18/7 2, 7, 9 1, 7, 1 7 cascade
[2, 2, 2], [2, 2, 2, 2, 2], [3, 5] 12/7 4, 6, 14 1, 1, 7 7 cascade
[2, 2, 2, 2, 2, 2, 2, 2], [4, 9] 45/7 9, 35 1, 7 7 cascade
[2, 4], [2, 2, 3], [2, 2, 2, 3, 2] 8/7 7, 7, 14 7, 7, 7 7 cascade
[2, 4], [2, 4], [2, 2, 2, 2, 2, 2] 9/7 7, 7, 7 7, 7, 1 7 cascade
[2], [2, 2, 2, 2, 2, 2, 2], [2, 5, 8] 40/7 2, 8, 70 1, 1, 7 7 cascade
[2, 2, 3], [2, 2, 2, 2, 2, 2], [3, 5] 8/7 7, 7, 14 7, 1, 7 7 cascade
[2, 2, 3], [2, 2, 2, 3, 2], [3, 3, 3] 6/7 7, 14, 21 7, 7, 7 7 cascade
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 11] 33/7 11, 21 1, 7 7 cascade
[2, 4], [2, 2, 2, 3, 2], [2, 2, 2, 2, 5] 6/7 7, 14, 21 7, 7, 7 7 cascade
[2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 10] 20/7 2, 10, 28 1, 1, 7 7 cascade
[2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [3, 2, 9] 18/7 3, 9, 42 1, 1, 7 7 cascade
[2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [4, 3, 8] 24/7 4, 8, 84 1, 1, 7 7 cascade
[2, 2, 2, 2, 2, 2], [3, 5], [2, 2, 2, 2, 5] 6/7 7, 14, 21 1, 7, 7 7 cascade
[3, 5], [2, 2, 2, 3, 2], [2, 2, 2, 2, 3, 3] 4/7 14, 14, 28 7, 7, 7 7 cascade
[2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 11] 12/7 3, 12, 21 1, 1, 7 7 cascade
[2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [4, 9] 10/7 5, 10, 35 1, 1, 7 7 cascade
[2, 2, 2, 2, 5], [2, 2, 2, 2, 5], [2, 2, 2, 2, 5] 3/7 21, 21, 21 7, 7, 7 7 cascade
[7], [7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 8/7 7, 7, 14 7, 7, 1 7 cascade
[14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 30/7 14, 15 7, 1 7 cascade
[2], [14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 16/7 2, 14, 16 1, 7, 1 7 cascade
[2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [8, 2, 8] 16/7 8, 8, 112 1, 1, 7 7 cascade
[2, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 11] 6/7 7, 14, 21 7, 1, 7 7 cascade
[2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [8, 8] 9/7 9, 9, 63 1, 1, 7 7 cascade
[3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 10] 4/7 14, 14, 28 7, 1, 7 7 cascade
[7], [14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 6/7 7, 14, 21 7, 7, 1 7 cascade
[2, 11], [2, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 3/7 21, 21, 21 7, 7, 1 7 cascade
[14], [14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] 4/7 14, 14, 28 7, 7, 1 7 cascade