A Combinatorial Approach to Involution and delta-Regularity II: Structure Analysis of Polynomial Modules with Pommaret Base

TL;DR

This paper introduces a combinatorial method for analyzing polynomial modules with Pommaret bases, focusing on involution, delta-regularity, and their connections to Castelnuovo-Mumford regularity and Noether normalization.

Contribution

It extends previous work by providing a detailed structural analysis of polynomial modules, especially emphasizing monomial ideals and their regularity properties.

Findings

Expanded treatment of monomial ideals and Castelnuovo-Mumford regularity

Established relations between delta-regularity and Noether normalization

Enhanced understanding of polynomial module structures with Pommaret bases

Abstract

Substantial changes in many parts of the paper. In particular, significantly expanded treatment of monomial ideals and of Castelnuovo-Mumford regularity. Also relation between delta-regularity and Noether normalisation now treated.