K3 surfaces

Geography of the K3 database

Click any number to get the K3 surfaces in the database with genus equal to the column heading and codimension the row heading.

-1 0 1 2 3 4 5 6 7 8 9 total
total 4281 6479 6627 6628
1 54 32 6 2 1 0 0 0 0 0 0 95
2 45 29 6 2 1 1 0 0 0 0 0 84
3 26 29 8 3 2 1 1 0 0 0 0 70
4 60 54 15 6 3 2 1 1 0 0 0 142
5 58 63 21 8 6 3 2 1 1 0 0 163
6 80 98 35 15 8 6 3 2 1 1 0 249
7 81 116 49 21 15 8 6 3 2 1 1 303
8 128 182 79 35
9 107 208 109 49
10 192 312 171 79
11 167 369 236 109
12 238 497 353 171
13 245 603 488 236
14 346 759 720 353
15 316 728 982 488
16 402 744 1419 720
17 337 581 1930 982
18 350 457 0 1419
19 266 267 0 1930
20 258 171 0 0
21 161 85 0 0
22 139 55 0 0
23 93 24 0 0
24 57 13 0 0
25 35 3 0 0
26 22 0 0 0
27 12 0 0 0
28 5 0 0 0
29 1 0 0 0

This table lists the number of K3 surfaces in the database by genus (across the top) and (estimated generic) codimension. Only those values indicated are stored in the database, although the list of K3 surfaces is infinite - the distribution of numbers by genus and codimension continues regularly to the right, with 6628 cases in each column following the pattern for genus 2 with codimension incremented by 1 at each new column. The paper below explains the meaning of this table in detail.

Authors and references

This data is provided by Selma Altinok, Gavin Brown, Anthony Iano-Fletcher, and Miles Reid.

Further details can be found in:

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