
TL;DR
This paper provides a complete numerical characterization of all extremal Betti numbers for graded submodules of finitely generated graded free modules over polynomial rings in characteristic zero.
Contribution
It introduces a comprehensive numerical framework to identify all possible extremal Betti numbers in this algebraic setting.
Findings
Characterization of extremal Betti numbers achieved
Applicable to all graded submodules of finitely generated free modules
Framework valid over polynomial rings in characteristic zero
Abstract
Let be a polynomial ring in variables over a field of characteristic . A numerical characterization of all possible extremal Betti numbers of any graded submodule of a finitely generated graded free -module is given.
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