Clearly, the discriminant should be positive on monotone choices of
parameters.
Based on the previous example and a few others, we conjecture
something much stronger.
Discriminant Conjecture
The discriminant of a polynomial system modeling Grassmannian
conditions on partial flags imposed by osculating flags lies in any
preorder generated by the differences s-t of the
parameters defining a monotone choice of points.
- Again, by the asymptotic result, this would imply the
Monotone Conjecture.
- We have computed some examples where the preorder of polynomials
positive on a monotone set of points is not finitely generated,
but the discriminant has the form of the conjecture.
