11 citations · 12 across the 4 of their papers we have counts for
6 papers
Thin polytopes: Lattice polytopes with vanishing local -polynomial
Christopher Borger, Andreas Kretschmer, Benjamin Nill
In this paper we study the novel notion of thin polytopes: lattice polytopes whose local -polynomials vanish. The local -polynomial is an important invariant in modern Eh…
Liftings of polynomial systems decreasing the mixed volume
Christopher Borger, Thomas Kahle, Andreas Kretschmer +2
The BKK theorem states that the mixed volume of the Newton polytopes of a system of polynomial equations upper bounds the number of isolated torus solutions of the system. Homotopy…
Inequalities between mixed volumes of convex bodies: volume bounds for the Minkowski sum
Gennadiy Averkov, Christopher Borger, Ivan Soprunov
In the course of classifying generic sparse polynomial systems which are solvable in radicals, Esterov recently showed that the volume of the Minkowski sum of -d…
Families of lattice polytopes of mixed degree one
Gabriele Balletti, Christopher Borger
It has been shown by Soprunov that the normalized mixed volume (minus one) of an -tuple of -dimensional lattice polytopes is a lower bound for the number of interior lattice…
Classification of triples of lattice polytopes with a given mixed volume
Gennadiy Averkov, Christopher Borger, Ivan Soprunov
We present an algorithm for the classification of triples of lattice polytopes with a given mixed volume in dimension 3. It is known that the classification can be reduced to t…
On defectivity of families of full-dimensional point configurations
Christopher Borger, Benjamin Nill
The mixed discriminant of a family of point configurations can be considered as a generalization of the -discriminant of one Laurent polynomial to a family of Laurent polynomial…