Comparing the sets of volume polynomials and Lorentzian Polynomials
Combinatorics
2026-01-14 v1 Algebraic Geometry
Abstract
Given n convex bodies in the real space of dimension d, we consider the set of homogeneous polynomials of degree d in n variables that can be represented as their volume polynomial. This set is a subset of the set of Lorentzian polynomials. Using our knowledge of operations that preserve the Lorentzian property, we give a complete classification of the cases when the two sets are equal.
Cite
@article{arxiv.2310.07020,
title = {Comparing the sets of volume polynomials and Lorentzian Polynomials},
author = {Amelie Menges},
journal= {arXiv preprint arXiv:2310.07020},
year = {2026}
}