A Minimal Poset Resolution of Stable Ideals
Timothy B.P. Clark
TL;DR
This paper constructs a minimal free resolution for stable monomial ideals using poset resolutions and CW complexes, providing a new combinatorial and topological approach to understanding their structure.
Contribution
It introduces a novel method to obtain minimal resolutions of stable ideals via poset and CW complex constructions, expanding the combinatorial tools available.
Findings
Constructed minimal free resolutions using poset of admissible symbols.
Identified a regular CW complex supporting the resolution.
Enhanced understanding of the structure of stable ideals.
Abstract
We use the theory of poset resolutions to construct the minimal free resolution of an arbitrary stable monomial ideal in the polynomial ring whose coefficients are from a field. This resolution is recovered by utilizing a poset of Eliahou-Kervaire admissible symbols associated to a stable ideal. The structure of the poset under consideration is quite rich and in related analysis, we exhibit a regular CW complex which supports a minimal cellular resolution of a stable monomial ideal.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models