Despite the filename, these computations are actually for the symmetric power of the universal curve, not rational tails. (* means there is a missing relation to make the ring Gorenstein) ---------------------------------------- n = 0 (regular FZ, so we know everything): g = 22: 1 1 2 3 5 7 11 15 21 25 29 25 21 15 11 7 5 3 2 1 1 g = 23: 1 1 2 3 5 7 11 15 21 27 32 32 27 21 15 11 7 5 3 2 1 1 g = 24: 1 1 2 3 5 7 11 15 22 28 36 38 37* 28 22 15 11 7 5 3 2 1 1 ---------------------------------------- n = 1: g = 18: 1 2 4 7 12 19 30 42 53 53 42 g = 19: 1 2 4 7 12 19 30 43 57 64 57 g = 20: 1 2 4 7 12 19 30 44 61 75 76* ---------------------------------------- n = 2: g = 15: 1 3 7 13 24 40 62 81 81 62 g = 16: 1 3 7 13 24 40 64 88 103 88 g = 17: 1 3 7 13 24 40 65 95 122 123* ---------------------------------------- n = 3: g = 12: 1 3 9 19 37 62 87 87 62 g = 13: 1 3 9 19 37 64 97 114 97 g = 14: 1 3 9 19 37 65 105 140 141* ---------------------------------------- n = 4: g = 9: 1 3 10 24 47 69 69 47 g = 10: 1 3 10 24 49 79 98 79 g = 11: 1 3 10 24 50 87 124 125* ---------------------------------------- n = 5: g = 8: 1 3 10 25 52 77 77 52 g = 9: 1 3 10 26 57 95 117 95 g = 10: 1 3 10 26 59 106 152 153* ---------------------------------------- n = 6: g = 7: 1 3 10 25 51 76 76 51 g = 8: 1 3 10 26 58 98 121 98 g = 9: 1 3 10 27 63 117 168 169* ---------------------------------------- n = 7: g = 6: 1 3 10 23 44 62 62 g = 7: 1 3 10 25 53 87 106 87 g = 8: 1 3 10 26 60 110 157 157 g = 9: 1 3 10 27 65 129 208 249* (Gor. rank is 248) ---------------------------------------- n = 8: (relation rank on top, Gorenstein rank on bottom) g = 6: 1 3 10 23 45 67 78 ? 1 3 10 23 45 67 78 67 g = 7: 1 3 10 25 54 93 127 ? 1 3 10 25 54 93 127 127 g = 8: 1 3 10 26 61 116 182 214 ? 1 3 10 26 61 116 182 214 182 ----------------------------------------