The functions starts with a random Prym canonical curve C of genus 7, say embedded by KC ⊗L. Then it picks randomly two points p,q on C such that the curve Cp=q of genus 8 obtained identifying p and q carries a two torsion line bundle Lpq such that Lpq pulls back to L under the normalization map C →Cp=q. The ideal of the curve Cp=q embedded by |K{Cp=q ⊗Lpq| is returned.
i1 : p=10007,kk=ZZ/p,R=kk[x_0..x_6]
o1 = (10007, kk, R)
o1 : Sequence
|
i2 : time I=randomOneNodalPrymCanonicalCurveOfGenus8(R);
-- used 10.4888 seconds
o2 : Ideal of R
|
i3 : (dim I,degree I, genus I)
o3 = (2, 14, 8)
o3 : Sequence
|
i4 : betti res I
0 1 2 3 4 5
o4 = total: 1 8 36 56 35 8
0: 1 . . . . .
1: . 7 1 . . .
2: . 1 35 56 35 8
o4 : BettiTally
|