We construct a curve C of genus 8 with a g27 together with a 2-torsion divisor. The model C’ of C in P2 has 7 double points. The divisor D0 will consist of eight points in which C’ and a rational quartic Q are tangent. We choose Q and C’ such that they have three double points in common. Since 7*4-3*22==2*8 there are no more intersection points. The divisor D1 will be given by the 8=7*2-3*2 additional intersection points of C’ with a conic defined by g1 through the 3 singular points. Note that D0-D1 is 2-torsion in Pic C.
i1 : p=10007;kk=ZZ/p; |
i3 : S=kk[x_0..x_2] o3 = S o3 : PolynomialRing |
i4 : time (I,D)=getSepticOfGenus8With2Torsion(S); -- used 0.386529 seconds |
i5 : dim I, degree I o5 = (2, 7) o5 : Sequence |
i6 : geometricGenus=genus I - degree ideal jacobian I o6 = 8 |