The Adjoint Polynomial of a Polyhedral Cone is a Covolume Polynomial
Commutative Algebra
2025-09-30 v2 Algebraic Geometry
Abstract
In this paper, we showed that the adjoint polynomial of a polyhedral cone equals the multidegree polynomial of the toric ideal with multigrading, both given by the vertex rays. This fact implies a conjecture of Aluffi, to the effect that the adjoint polynomial of a polyhedral cone in the positive orthant is a covolume polynomial.
Keywords
Cite
@article{arxiv.2509.20606,
title = {The Adjoint Polynomial of a Polyhedral Cone is a Covolume Polynomial},
author = {Guanxi Li},
journal= {arXiv preprint arXiv:2509.20606},
year = {2025}
}