We follow the random construction of an element of the family from Thm 4.7 or Thm 4.8 as explained in Matrix factorizations and families of curves of genus 15
i1 : kk=ZZ/10007;S=kk[x_0..x_4]; |
i3 : N=constructEx5(S); |
i4 : betti res N 0 1 2 3 o4 = total: 6 13 12 5 3: 6 11 . . 4: . 2 12 4 5: . . . 1 o4 : BettiTally |
i5 : E=annihilator N; (degree E,genus E)==(14,15) o5 : Ideal of S o6 = true |
i7 : (M0,M1)=matrixFactorizationFromModule(N); |
i8 : tangentKernelDimension(N,M0)==6 o8 = true |
i9 : betti res annihilator N 0 1 2 3 o9 = total: 1 6 10 5 0: 1 . . . 1: . 1 . . 2: . 2 . . 3: . 3 10 5 o9 : BettiTally |
i10 : N=constructEx5(S,{(4,1)}); |
i11 : betti res N 0 1 2 3 o11 = total: 6 13 12 5 3: 6 11 . . 4: . 2 12 4 5: . . . 1 o11 : BettiTally |
i12 : E=annihilator N; (degree E,genus E)==(14,16) o12 : Ideal of S o13 = true |
i14 : (M0,M1)=matrixFactorizationFromModule(N); |
i15 : tangentKernelDimension(N,M0)==10 o15 = true |
i16 : betti res annihilator N 0 1 2 3 o16 = total: 1 4 5 2 0: 1 . . . 1: . 1 . . 2: . 3 1 . 3: . . 4 1 4: . . . 1 o16 : BettiTally |
i17 : N=constructEx5(S,14); |
i18 : betti res N 0 1 2 3 o18 = total: 5 12 13 6 0: 1 . . . 1: 4 12 2 . 2: . . 11 6 o18 : BettiTally |
i19 : E=annihilator N; (degree E,genus E)==(14,14) o19 : Ideal of S o20 = true |
i21 : (M0,M1)=matrixFactorizationFromModule(N); |
i22 : tangentKernelDimension(N,M0)==4 o22 = true |
i23 : betti res annihilator N 0 1 2 3 o23 = total: 1 6 9 4 0: 1 . . . 1: . . . . 2: . 6 3 . 3: . . 6 4 o23 : BettiTally |