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PrymCanonicalCurves :: randomOneNodalPrymCanonicalCurveOfGenus8

randomOneNodalPrymCanonicalCurveOfGenus8 -- pick a random Prym canonical curve of arithmetic genus 8 with one node

Synopsis

Description

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

Ways to use randomOneNodalPrymCanonicalCurveOfGenus8 :