The function constructs a general curve C of genus 12 and degree 14 in P4 with randomGenus12Degree14CurveInP4 and constructs its canonical embedding in P11. By construction, if H is an hyperplane divisor in P4, then KC - H is a g18. The function returns a sequence (I, H1, H2), where I is the ideal of the canonically embedded curve in P11 and H1 and H2 are the hyperplanes passing through 14 points on the curve corresponding to H via the canonical embedding. A general linear combination of H1 and H2 cuts the curve in these 14 points plus 8 points corresponding to the g18. By construction, this procedure is rational and dominant.
i1 : p=32009; |
i2 : time (I, H1, H2)=randomGenus12Degree8CoverOfP1(p);
-- used 24.7687 seconds
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i3 : genus I, degree I o3 = (12, 22) 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 ]
32009 0 1 2 3 4 5 6 7 8 9 10 11
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i5 : codim K, degree K o5 = (11, 22) o5 : Sequence |
i6 : IH=I+ideal (H1)+ideal (H2); -- 2g-2-8=14 fixed points
ZZ
o6 : Ideal of -----[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
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i7 : codim IH, degree IH o7 = (11, 14) o7 : Sequence |
i8 : KmH=K:IH; -- 8 moving points corresponding to the g^1_8
ZZ
o8 : Ideal of -----[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
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i9 : codim KmH, degree KmH o9 = (11, 8) o9 : Sequence |