Resurgence number of matroid configuration

TL;DR

This paper establishes new upper bounds and formulas for the resurgence number of symbolic powers in matroidal configurations, including special cases like peaked simplicial complexes and generalized uniform matroids.

Contribution

It introduces a unified approach to compute the resurgence number for various matroidal configurations, extending known results to more complex structures.

Findings

New upper bounds for resurgence number in matroidal configurations

A closed-form formula for computing resurgence number

Analysis of strict containment in generalized uniform matroidal configurations

Abstract

This article gives a new upper bound for the resurgence number of symbolic powers of matroidal configuration in the following situations: the height of the matroidal configuration is big, or the height is small, and the corresponding simplicial complex of the matroidal configuration is peaked. The Peaked simplicial complex is a generalization of bipartite graph. Furthermore, the article also gives a clean formula to compute the resurgence number and the strict containment of generalized uniform matroidal configuration which includes case of star configuration of hypersurfaces.