Squarefree monomial modules and extremal Betti numbers

TL;DR

This paper investigates the structure of squarefree monomial submodules in graded free modules over polynomial rings and analyzes their extremal Betti numbers to understand their algebraic properties.

Contribution

It introduces a study of specific classes of squarefree monomial submodules and examines their Betti tables to explore extremal Betti numbers.

Findings

Characterization of extremal Betti numbers for these modules

Insights into the algebraic structure of squarefree monomial modules

Potential applications in combinatorial algebra

Abstract

Let K be a field and S a polynomial ring in a finite number of variables over K. Let F be a finitely generated graded free S-module. 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.