Squarefree Monomial Modules and Extremal Betti Numbers

Let K be a field and let S = K[x(1),...,x(n)] be a polynomial ring over K. Let F = circle plus(r)(i-1) Se-i be a finitely generated graded free S-module with basis {e(1),...,e(r)} in degrees f(1),...f(r) such that f(1) <= f(2) <= ... <= f(r). We examine some classes of squarefree monomial submodules of F. Hence, we focalize our attention on the Betti table of such classes in order to analyze the behavior of their extremal Betti numbers.