Minimal Resolutions of Some Monomial Submodules

Abstract.

Let K be a field and let $S = K[x_1, \ldots , x_n]$ be the polynomial ring over K. Let $F = \bigoplus^r_{i=1} Se_{i}$ be a finitely generated graded free S-module with basis $e_1, \ldots , e_r$ in degrees $f_1, \ldots , f_r$ renumbered as necessary so that $f_1 \leq f_2 \leq \cdots \leq f_r$. We study the behaviour of the extremal Betti numbers of special classes of monomial submodules of F, for r > 1.