The dilatation process step by step
Ki,j denotes the complex after the i-th
blowup with intersection form of signature j.
Click on .gap to
see the complex in GAP notation, click on .poly for the polymake format.
| blowup |
Euler char. |
2nd Betti number |
complexes Ki,j |
| 0 |
8 |
6 |
K0,0 | .gap | .poly |
| | |
| | |
| 1 |
9 |
7 |
K1,1 | .gap | .poly |
| | |
| | |
| 2 |
10 |
8 |
K2,2 | .gap | .poly |
| | |
| | |
| 3 |
11 |
9 |
K3,3 | .gap | .poly |
| | |
| | |
| 4 |
12 |
10 |
K4,4 | .gap | .poly |
| | |
| | |
| 5 |
13 |
11 |
K5,5 | .gap | .poly |
| | |
| | |
| 6 |
14 |
12 |
K6,6 | .gap | .poly |
K6,4 | .gap | .poly |
| | |
| 7 |
15 |
13 |
K7,7 | .gap | .poly |
K7,3 | .gap | .poly |
| | |
| 8 |
16 |
14 |
K8,8 | .gap | .poly |
K8,4 | .gap | .poly |
| | |
| 9 |
17 |
15 |
K9,9 | .gap | .poly |
K9,3 | .gap | .poly |
K9,5 | .gap | .poly |
| 10 |
18 |
16 |
K10,10 | .gap | .poly |
K10,4 | .gap | .poly |
K10,6 | .gap | .poly |
| 11 |
19 |
17 |
K11,11 | .gap | .poly |
K11,3 | .gap | .poly |
K11,5 | .gap | .poly |
| 12 |
20 |
18 |
K12,12 | .gap | .poly |
K12,2 | .gap | .poly |
K12,6 | .gap | .poly |
| 13 |
21 |
19 |
K13,13 | .gap | .poly |
K13,1 | .gap | .poly |
K13,5 | .gap | .poly |
| 14 |
22 |
20 |
K14,14 | .gap | .poly |
K14,2 | .gap | .poly |
K14,4 | .gap | .poly |
| 15 |
23 |
21 |
K15,15 | .gap | .poly |
K15,1 | .gap | .poly |
K15,3 | .gap | .poly |
| 16 |
24 |
22 |
K16,16 | .gap | .poly |
K16,0 | .gap | .poly |
K16,4 | .gap | .poly |
> > download all complexes (.zip, 229.6kB)
K16,16 is a K3 surface,
K16,0 is a connected sum of complex projective planes
of the form 11(CP2) # 11(-CP2) and
K16,4 is a connected sum of complex projective planes
of the form 13(CP2) # 9(-CP2).
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