Reid's theorem says that the set of maximal isotropic subspaces on a complete intersection of two quadrics in (2g+2) variables is isomorphic to the set of degree 0 line bundles on the associated hyperelliptic curve E of genus g. The method computes the maximal isotropic subspace uL corresponding to the translation of u by L.
i1 : kk=ZZ/101; |
i2 : g=2; |
i3 : (S,qq,R,u, M1,M2, Mu1,Mu2) = randomNicePencil(kk,g); |
i4 : M=cliffordModule (Mu1, Mu2, R); |
i5 : f=M.hyperellipticBranchEquation 5 4 2 3 3 2 4 5 6 o5 = 15s t + 6s t + 33s t + 30s t - 48s*t + 14t o5 : R |
i6 : L=randomLineBundle(0,f); |
i7 : uL=translateIsotropicSubspace(M,L,S) o7 = | y_1-36z_1-2z_2 y_0+20z_1+17z_2 x_1+25z_1-12z_2 x_0+40z_1-43z_2 | 1 4 o7 : Matrix S <--- S |
i8 : assert (betti uL == betti u) |
The object translateIsotropicSubspace is a method function.