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 $F$.

A constructive method for standard borel fixed submodules with given extremal Betti numbers

Crupi, Marilena
2017

Abstract

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 $F$.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3119492
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