The function gives a plane curve of degree 8 with 10 ordinary double points, such that the pencils of lines through each double points cut out 10 pencils on its canonical model, and results in the Betti number B(5,6)=50.
i1 : p=101; |
i2 : (G,Ican)=random6gonalGenus11Curve10Pencil(p); |
i3 : genus Ican, degree Ican o3 = (11, 20) o3 : Sequence |
i4 : Fres=res(Ican, FastNonminimal => true); |
i5 : betti(Fres, Minimize=>true)
0 1 2 3 4 5 6 7 8 9
o5 = total: 1 36 160 315 338 338 315 160 36 1
0: 1 . . . . . . . . .
1: . 36 160 315 288 50 . . . .
2: . . . . 50 288 315 160 36 .
3: . . . . . . . . . 1
o5 : BettiTally
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