Cellular structure of the Pommaret-Seiler resolution for quasi-stable ideals (Q6602401)

Among the most important features of Groebner bases that relate the properties of polynomial ideals to those of monomial ideals, there is the ability to derive a free resolution of a polynomial ideal from that of a monomial ideal, although the resolution may not always be minimal. In the context of involutive divisions, other types of polynomial ideal generators with similar properties also exist. This paper investigates the resolution properties of quasi-stable ideals through involutive bases theory and cellular topology, giving interesting contributions.\N\NThe authors prove that the Pommaret-Seiler resolution for quasi-stable ideals is cellular, and they explicitly construct its cellular structure. Consequently, the Pommaret-Seiler resolution is shown to generalize the Eliahou-Kervaire resolution even for having a cellular structure. Moreover, Discrete Morse Theory is applied to reduce the resolution to its minimal form when necessary.