Stability of Associated Primes and Depth of Integral Closures of Powers of Edge Ideals

TL;DR

This paper investigates the stability properties of associated primes and depth of integral closures of powers of edge ideals, providing bounds on the powers for which these properties remain unchanged.

Contribution

It establishes sharp bounds on the powers of edge ideals where associated primes and depth of their integral closures stabilize, advancing understanding of their algebraic behavior.

Findings

Sharp bounds for stability of associated primes

Sharp bounds for stability of depth of integral closures

Enhanced understanding of algebraic properties of edge ideals

Abstract

In this paper, we study associated primes and depth of integral closures of powers of edge ideals. We provide sharp bounds on how big of powers for which the set of associated primes and the depth of integral closures of powers of edge ideals are stable.