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arXiv · 2509.20606

The Adjoint Polynomial of a Polyhedral Cone is a Covolume Polynomial

Guanxi Li
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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.

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Guanxi Li. 2025-09-24. The Adjoint Polynomial of a Polyhedral Cone is a Covolume Polynomial. https://arxiv.org/abs/2509.20606

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