A duality theorem for the ic-resurgence of edge ideals

Abstract

The aim of this work is to use linear programming and polyhedral geometry to prove a duality formula for the ic-resurgence of edge ideals. We show that the ic-resurgence of the edge ideal $I$ of a clutter $\mathcal{C}$ and the ic-resurgence of the edge ideal $I^{\vee }$ of the blocker ${\mathcal{C}}^{\vee }$ of $\mathcal{C}$ coincide. If $\mathcal{C}$ is the clutter of bases of certain uniform matroids, we recover a formula for the resurgence of $I$, and if $\mathcal{C}$ is a connected non-bipartite graph with a perfect matching, we show a formula for the Waldschmidt constant of $I^{\vee }$.

References in corpus (3)

• Integral closures of monomial ideals and Fulkersonian hypergraphs
• Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals
• Consequences of the packing problem