On the containment hierarchy for simplicial ideals

TL;DR

This paper investigates the containment relations and asymptotic invariants of simplicial ideals generated by hyperplane arrangements in projective space, providing insights into their algebraic and geometric properties.

Contribution

It introduces new results on the containment hierarchy and asymptotic behavior of simplicial ideals associated with hyperplane arrangements.

Findings

Established containment relations for simplicial ideals.

Analyzed asymptotic invariants of these ideals.

Provided conditions for ideal containments in projective space.

Abstract

The purpose of this note is to study containment relations and asymptotic invariants for ideals of fixed codimension skeletons (simplicial ideals) determined by arrangements of $n + 1$ general hyperplanes in the $n-$dimensional projective space over an arbitrary field.