A constructive method for standard Borel fixed submodules with given extremal Betti numbers
Summary: Let \(S\) be a polynomial ring in \(n\) variables over a field \(K\) of any characteristic. Given a strongly stable submodule \(M\) of a finitely generated graded free \(S\)-module \(F\), we propose a method for constructing a standard Borel-fixed submodule \(\widetilde{M}\) of \(F\) so that the extremal Betti numbers of \(M\), values as well as positions, are preserved by passing from \(M\) to \(\widetilde{M}\). As a result, we obtain a numerical characterization of all possible extremal Betti numbers of any standard Borel-fixed submodule of a finitely generated graded free \(S\)-module \(F\).
scientific article; zbMATH DE number 6898685
scientific article