Computing general strongly stable modules with given extremal Betti numbers

Abstract

Let $S$ be a polynomial ring in $n$ variables over a field $K$ of any characteristic. Let $M$ be a strongly stable submodule of a finitely generated graded free $S$-module $F$, with all basis elements of $F$ of the same degree. The existence of a general strongly stable submodule $\tilde{M}$ of a finitely generated graded free $S$-module $\tilde{F}$, $rank\tilde{F}\ge rankF$, which preserves values and positions of the extremal Betti numbers of $M$, is proved.