The monomial glicci conjecture

Let $\mathbb K$ be a field, let $R=\mathbb K[x_1,\ldots,x_n]$, and let $I\subseteq R$ be a Cohen--Macaulay monomial ideal. Monomial glicci conjecture. The ideal $I$ is glicci, meaning that it lies in the Gorenstein liaison class of a complete intersection. This conjecture would answer affirmatively the open question of whether all Cohen--Macaulay ideals are glicci in the monomial case; the paper's results establish substantial classes of Cohen--Macaulay monomial ideals with this property, but do not resolve the general statement.