  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.
