The Solomon–Terao polynomial order-degree conjecture for multiarrangements

Let $({\mathcal{A}},m)$ be a tame multiarrangement of rank $\ell$, and let $U_{d+1}({\mathcal{A}})$ denote the set of generic elements used to define the Solomon–Terao algebra. For $\eta\in U_{d+1}({\mathcal{A}})$, let $ST_{d+1}({\mathcal{A}};x)$ be the Solomon–Terao polynomial of order $d+1$.

Solomon–Terao order-degree conjecture. If $\eta\in U_{d+1}({\mathcal{A}})$, then $ST_{d+1}({\mathcal{A}};x)$ is monic of degree

$$|{\mathcal{A}}|+\ell(d-1).$$

This is presented as the conjecture on the top-degree monomials of the Solomon–Terao polynomials, recalling a conjecture from AMMN. The preceding theorem establishes the relevant Hilbert-series description for tame multiarrangements, but the stated monicity and degree formula remain unresolved in the supplied text.