This is an irresponsible question: I do not have done any thinking on it, or even literature search.


I just became curious whether there is some modification of the notion of a common root of two polynomials which would be detected by a Pfaffian of some alternate matrix, rather than a determinant of some general matrix, like it is the case with the resultant.


(PS Seems like there is no tag "algebra", so I chose commutative algebra instead)



Determinant is to Pfaffian as resultant is to what?
Pfaffian resultant formulas are obtained in [Resultants and Chow forms via Exterior Syzygies](https://arxiv.org/abs/math/0111040) (2001), where the polynomials are represented by coordinates on a Grassmanian manifold.


