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On defectivity of families of full-dimensional point configurations | | Christopher Borger
; Benjamin Nill
; | | Date: |
23 Jan 2018 | | Abstract: | The mixed discriminant of a family of point configurations is a
generalization of the $A$-discriminant of a 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 conjecture by Cattani, Cueto, Dickenstein,
Di Rocco and Sturmfels that a family of $n$ full-dimensional configurations in
$mathbb{Z}^n$ is defective if and only if the mixed volume of the convex hulls
of its elements is $1$. | | Source: | arXiv, 1801.7467 | | Services: | Forum | Review | PDF | Favorites | |
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