The function gives a plane curve of degree 9 with 4 triple, and and 5 ordinary double points passing through the k-5 points among the ninth fixed points of the pencil of cubics through the 4 triple points, and and 4 chosen nodes by omitting one of them. The canonical model of this curve carries k pencils of degree 6, such that the Betti number B(5,6)=5k.
i1 : p=nextPrime 10^3; |
i2 : time L=random6gonalGenus11CurvekPencil(p,5);
-- used 2.66014 seconds
|
i3 : Ican=L_4;
ZZ
o3 : Ideal of ----[r , r , r , r , r , r , r , r , r , r , r ]
1009 0 1 2 3 4 5 6 7 8 9 10
|
i4 : genus Ican, degree Ican o4 = (11, 20) o4 : Sequence |
i5 : Fres=res(Ican, FastNonminimal => true); |
i6 : betti(Fres, Minimize=>true)
0 1 2 3 4 5 6 7 8 9
o6 = total: 1 36 160 315 313 313 315 160 36 1
0: 1 . . . . . . . . .
1: . 36 160 315 288 25 . . . .
2: . . . . 25 288 315 160 36 .
3: . . . . . . . . . 1
o6 : BettiTally
|
i7 : setRandomSeed" " o7 = 32 |
i8 : p=nextPrime 10^4; |
i9 : time L=random6gonalGenus11CurvekPencil(p,9);
-- used 2.75217 seconds
|
i10 : Ican=L_4;
ZZ
o10 : Ideal of -----[r , r , r , r , r , r , r , r , r , r , r ]
10007 0 1 2 3 4 5 6 7 8 9 10
|
i11 : genus Ican, degree Ican o11 = (11, 20) o11 : Sequence |
i12 : Fres=res(Ican, FastNonminimal => true); |
i13 : betti(Fres, Minimize=>true)
0 1 2 3 4 5 6 7 8 9
o13 = total: 1 36 160 315 333 333 315 160 36 1
0: 1 . . . . . . . . .
1: . 36 160 315 288 45 . . . .
2: . . . . 45 288 315 160 36 .
3: . . . . . . . . . 1
o13 : BettiTally
|