Abstract:
Let K be a field, S=K[x1,…,xn], the polynomial ring over K, and let F be a finitely generated graded free S-module with homogeneous basis. Certain invariants, such as the Castelnuovo–Mumford regularity and the graded Betti numbers of submodules of F, are studied; in particular, the componentwise linear submodules of F are characterized in terms of their graded Betti numbers.