The function gives a plane curve of degree 9 with 3 triple, and 8 ordinary double points, such that pencil of lines through each of the triple points, and the pencil of cubics through the triple points, and five chosen double points by omitting two of them cut out 4 pencils of degree 6 on its canonical model.
i1 : setRandomSeed"" o1 = 0 |
i2 : p=nextPrime 10^3; |
i3 : (G,Ican)=random6gonalGenus11Curve4Pencil(p); |
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 36 160 315 308 308 315 160 36 1
0: 1 . . . . . . . . .
1: . 36 160 315 288 20 . . . .
2: . . . . 20 288 315 160 36 .
3: . . . . . . . . . 1
o6 : BettiTally
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