On defectivity of families of full-dimensional point configurations

Christopher Borger, Benjamin Nill
2020 Proceedings of the American Mathematical Society, Series B  
The mixed discriminant of a family of point configurations can be considered as a generalization of the A-discriminant of one Laurent polynomial to a family of Laurent polynomials. Generalizing the concept of defectivity, a family of point configurations is called defective if the mixed discriminant is trivial. Using a recent criterion by Furukawa and Ito we give a necessary condition for defectivity of a family in the case that all point configurations are full-dimensional. This implies the
more » ... This implies the conjecture by Cattani, Cueto, Dickenstein, Di Rocco, and Sturmfels that a family of n full-dimensional configurations in Z n is defective if and only if the mixed volume of the convex hulls of its elements is 1.
doi:10.1090/bproc/46 fatcat:skoicxcdwjguphhzejnmuv6zwy