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translateIsotropicSubspace -- choose a random isotropic subspace

Synopsis

Description

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 : setRandomSeed 0

o2 = 0
i3 : g=2;
i4 : (S,qq,R,u, M1,M2, Mu1,Mu2) = randomNicePencil(kk,g);
i5 : M=cliffordModule (Mu1, Mu2, R);
i6 : f=M.hyperellipticBranchEquation

        5      4 2      3 3      2 4        5      6
o6 = 15s t + 6s t  + 33s t  + 30s t  - 48s*t  + 14t

o6 : R
i7 : L=randomLineBundle(0,f);
i8 : uL=translateIsotropicSubspace(M,L,S)

o8 = | y_1+28z_1+48z_2 y_0+16z_1-21z_2 x_1-18z_1+25z_2 x_0-15z_2 |

             1      4
o8 : Matrix S  <-- S
i9 : assert (betti uL == betti u)

See also

Ways to use translateIsotropicSubspace:

For the programmer

The object translateIsotropicSubspace is a method function.