Regularity of Canonical and Deficiency modules for Monomial ideals

TL;DR

This paper proves that the Castelnuovo--Mumford regularity of canonical and deficiency modules for monomial ideals is bounded by their dimension, providing new insights into their algebraic structure.

Contribution

It establishes a dimension-based bound on the regularity of canonical and deficiency modules for monomial ideals, a novel result in commutative algebra.

Findings

Regularity of modules is bounded by their dimension.

The result applies specifically to monomial ideals.

Provides a new bound for algebraic invariants.

Abstract

We show that the Castelnuovo--Mumford regularity of the canonical or a deficiency module of the quotient of a polynomial ring by a monomial ideal is bounded by its dimension.