The function constructs a general curve C of genus 13 and degree 17 in P6 with randomGenus13Degree17CurveInP6 and constructs its canonical embedding in P12. By construction, if H is an hyperplane divisor in P6, then KC - H is a g17. The function returns a sequence (I, H1, H2), where I is the ideal of the canonically embedded curve in P12 and H1 and H2 are the hyperplanes passing through 17 points on the curve corresponding to H via the canonical embedding. A general linear combination of H1 and H2 cuts the curve in these 17 points plus 7 points corresponding to the g17. By construction, this procedure is rational and dominant.
i1 : p=32009; |
i2 : time (I, H1, H2)=randomGenus13Degree7CoverOfP1(p);
-- used 21.5907 seconds
|
i3 : genus I, degree I o3 = (13, 24) o3 : Sequence |
i4 : K=I+ideal(random(ZZ)*H1+random(ZZ)*H2);
ZZ
o4 : Ideal of -----[x , x , x , x , x , x , x , x , x , x , x , x , x ]
32009 0 1 2 3 4 5 6 7 8 9 10 11 12
|
i5 : codim K, degree K o5 = (12, 24) o5 : Sequence |
i6 : IH=I+ideal (H1)+ideal (H2); -- 2g-2-7=17 fixed points
ZZ
o6 : Ideal of -----[x , x , x , x , x , x , x , x , x , x , x , x , x ]
32009 0 1 2 3 4 5 6 7 8 9 10 11 12
|
i7 : codim IH, degree IH o7 = (12, 17) o7 : Sequence |
i8 : KmH=K:IH; -- 7 moving points corresponding to the g^1_7
ZZ
o8 : Ideal of -----[x , x , x , x , x , x , x , x , x , x , x , x , x ]
32009 0 1 2 3 4 5 6 7 8 9 10 11 12
|
i9 : codim KmH, degree KmH o9 = (12, 7) o9 : Sequence |