The only problem with this straightforward analysis
is that the given formulation is infeasible:
Fgen has 9 homogeneous
parameters,
so computations are over the field
Q(C22, C21, ...,
C00).
Such a computation is just not possible.
Solution: Geometry.
The automorphism group of the product
l1xl2 has dimension 6
We find a 2-dimensional family of (2,2)-forms
F(s,t) =
s w2z2
+ (1-s) wxz2
- 2 wxyz
+ (1-t) wxy2
+ t x2y2
whose orbit under this automorphism group is dense in
P8.
If we instead use the system
F(s,t) = FQ,
then we can apply our previous analysis, working now with the parameters
s,t over the field
Q(s,t).
Theorem.
After removing the excess components from the ideal given by the equations
F(s,t) = FQ,
we have an ideal
I
defining a curve of degree 24 in the projective space
P9Q(s,t)
of quadrics.
Which curve of degree 24 ?
