This paper shows that the adjoint polynomial equals the multidegree polynomial of the toric ideal, indicating a significant mathematical relationship.
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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Guoyin Li (2025) studied this question.
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