Simplicial complexes and minimal free resolution of monomial algebras
Ignacio Ojeda, A. Vigneron-Tenorio
TL;DR
This paper explores how the combinatorics of simplicial complexes can be used to explicitly describe the minimal free resolutions of certain monomial algebras, including toric rings, providing an algorithmic approach.
Contribution
It introduces a combinatorial method linking simplicial complexes to the minimal free resolutions of monomial algebras, including an algorithmic procedure.
Findings
Explicit combinatorial description of resolutions
Algorithmic procedure for partial computation
Applicable to toric rings and related algebras
Abstract
This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those algebras is related to the combinatorics of some simplicial complexes. Our description may be interpreted as an algorithmic procedure to partially compute this resolution.
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