Fano 3-folds

Geography of the Fano 3-fold database

Click any number to get the Fano 3-folds of Fano index 1 in the database with genus equal to the column heading and codimension the row number.

-2 -1 0 1 2 3 4 5 6 7 8-37 total
total 264 4527 6166 5244 4319 3555 2912 2386 1955 1594 6628 39550
1 54 32 6 2 1 95
2 1 45 29 6 2 1 1 85
3 26 29 8 3 2 1 1 70
4 3 60 54 15 6 3 2 1 1 145
5 1 58 63 21 8 6 3 2 1 1 164
6 4 80 98 35 15 8 6 3 2 1 1 253
7 81 116 49 21 15 8 6 3 2 2 303
8 6 128 182 79 35 21 15 8 6 3 4 487
9 3 107 208 109 49 35 21 15 8 6 7 568
10 10 194 314 171 79 49 35 21 15 8 13 909
11 5 168 378 236 109 79 49 35 21 15 21 1116
12 7 244 538 353 171 109 79 49 35 21 36 1642
13 8 254 638 485 236 171 109 79 49 35 57 2121
14 11 377 879 698 353 236 171 109 79 49 92 3054
15 10 349 889 870 480 351 236 171 109 79 141 3685
16 15 509 802 998 675 473 349 235 171 109 220 4556
17 21 501 480 740 786 637 456 342 233 171 329 4696
18 17 604 284 318 773 658 571 427 331 228 498 4709
19 23 465 103 43 401 516 488 474 380 308 716 3917
20 31 220 44 4 106 159 267 299 345 308 962 2745
21 32 3 5 8 24 42 101 137 202 1070 1624
22 27 1 1 1 3 7 28 43 918 1029
23 13 1 1 5 612 632
24 10 377 387
25 4 229 233
26 2 139 141
27-35 184 184

This table lists the number of Fano 3-folds of Fano index 1 in the database by genus (across the top) and (estimated generic) codimension.

Authors and references

This data is provided by Selma Altinok, Gavin Brown, Anthony Iano-Fletcher, Miles Reid, and Kaori Suzuki. Warning: the lists of Fanos of index > 2 are under construction. They are classifications of basket-genus pairs, and will be refined following results of Prokhorov and Reid.

Further details can be found in:

Please cite one of the above references if you use this data.