The stable set of associated primes of a complementary edge ideal

TL;DR

This paper explicitly characterizes the associated primes of all powers of a complementary edge ideal, proves their persistence, and analyzes their homological properties, advancing understanding of monomial ideal structures.

Contribution

It provides a complete description of associated primes and homological properties of powers of complementary edge ideals, including the v-function and persistence property.

Findings

Associated primes of all powers are explicitly determined.

Associated primes satisfy the persistence property.

Homological properties of powers of squarefree monomial ideals are fully described.

Abstract

We explicitly determine the associated primes of every power of a complementary edge ideal, prove that they satisfy the persistence property, and compute the $\text{v}$-function. In the course of the proofs, we completely describe the homological properties of all powers of squarefree monomial ideals generated in degrees large relative to the number of variables defining them.