Monomial ideals and the Gorenstein liaison class of a complete intersection

In an earlier work, the authors described a mechanism for lifting monomial ideals to reduced unions of linear varieties. When the monomial ideal is Cohen-Macaulay (including Artinian), the corresponding union of linear varieties is arithmetically Cohen-Macaulay. The first main result of this paper is that if the monomial ideal is Artinian then the corresponding union is in the Gorenstein linkage class of a complete intersection (glicci). This technique has some interesting consequences. For instance, given any (d + 1)-times differentiable O-sequence H, there is a nondegenerate arithmetically Cohen-Macaulay reduced union of linear varieties with Hilbert function H which is glicci. In other words, any Hilbert function that occurs for arithmetically Cohen-Macaulay schemes in fact occurs among the glicci schemes. This is not true for licci schemes. Modifying our technique, the second main result is that any Cohen-Macaulay Borel-fixed monomial ideal is glicci. As a consequence, all arithmetically Cohen-Macaulay subschemes of projective space are glicci up to flat deformation.