On monomial ideals whose Lyubeznik resolution is minimal

TL;DR

This paper characterizes Lyubeznik ideals, which are monomial ideals whose Lyubeznik resolution is minimal, and identifies specific classes of such ideals, advancing understanding of their algebraic structure.

Contribution

The paper provides a complete characterization of Lyubeznik ideals and identifies new classes of these ideals, enriching the theory of minimal free resolutions.

Findings

Characterization of Lyubeznik ideals

Identification of classes of Lyubeznik ideals

Conditions for minimal Lyubeznik resolutions

Abstract

For a monomial ideal $I$, let $G(I)$ be its minimal set of monomial generators. If there is a total order on $G(I)$ such that the corresponding Lyubeznik resolution of $I$ is a minimal free resolution of $I$, then $I$ is called a Lyubeznik ideal. In this paper, we characterize the Lyubeznik ideals, and we discover some classes of Lyubeznik ideals.