Geometric description of lifting monomial ideals

By focusing our attention on the set of monomials outside a given monomial ideal, we tackle the study of the geometric configurations of (reduced) unions of projective linear varieties arising from lifting monomial ideals via a classic lifting procedure, called t-lifting, and a more general lifting procedure, called pseudo-t-lifting. We observe that, in contrast to the Artinian case, in the positive dimensional case we may not obtain generalized stick figures also via a generic pseudo-t-lifting. In particular, in dimension 1 a generic pseudo-1-lifting produces a seminormal union of lines. Then we give conditions to obtain generalized stick figures by means of pseudo-t-liftings of non-Artinian monomial ideals.