On CW complexes supporting Eliahou-Kervaire type resolutions of Borel fixed ideals

TL;DR

This paper demonstrates that certain algebraic resolutions of Borel fixed ideals are supported by regular CW complexes with underlying spaces that are closed balls, extending to Cohen-Macaulay cases.

Contribution

It proves that Eliahou-Kervaire resolutions of Cohen-Macaulay stable monomials are supported by regular CW complexes that are closed balls, and extends this to variants of Borel fixed ideals.

Findings

Supports of resolutions are regular CW complexes.

Underlying spaces are closed balls in Cohen-Macaulay cases.

Extensions to variants like squarefree strongly stable ideals.

Abstract

We prove that the Eliahou-Kervaire resolution of a Cohen-Macaulay stable monomial is supported by a regular CW complex whose underlying space is a closed ball. We also show that the modified Eliahou-Kervaire resolutions of variants of a Borel fixed ideal (e.g., a squarefree strongly stable ideal) are supported by regular CW complexes, and their underlying spaces are closed balls in the Cohen-Macaulay case.