Multigraded modules of nested type

Abstract

Extending the notion of monomial ideals of nested type, we introduce multigraded modules of nested type. We characterize them algebraically, resulting in the explicit construction of their dimension filtration. We compute several important invariants, including their Castelnuovo-Mumford regularity and projective dimension without {us\nobreak {ing}} the construction of their minimal graded free resolution. We show that they are pretty clean and hence sequentially Cohen-Macaulay.