Slightly mixed symbolic powers of matroids are locally glicci

Let $\text{M}$ be a matroid, and let $I_{\text{M}}$ be either the Stanley–Reisner or the cover ideal of $\text{M}$. In this paper we prove that for any matroid $\text{M}$ on $[n]$, any $\mathrm{\ell }\in {\text{ZZ}}_{+}$, and any squarefree monomial $N\in R=\text{kk}[x_1,\dots ,x_n]$, the ideal $I_{\text{M}}^{(\mathrm{\ell })}:N$, which we call a ``slightly mixed symbolic power" of $I_{\text{M}}$, is always Cohen–Macaulay and locally glicci. As a corollary, we obtain that all symbolic powers $I_{\text{M}}^{(\mathrm{\ell })}$ are locally glicci.