Monomial ideals admit pivot resolutions that sit between Lyubeznik and Taylor resolutions, always carry a DG-algebra structure, and come with explicit Eisenbud-Shamash higher homotopies over complete intersections.
Resolutions of modules with initially linear syzygies
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abstract
We introduce the class of modules with initially linear syzygies, which includes ideals with linear quotients, and study their minimal resolutions. Using a contracting homotopy for the resolutions, we see that the minimal resolution of a matroidal monomial ideal admits a DGA structure.
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2024 1verdicts
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A family of simplicial resolutions which are DG-algebras
Monomial ideals admit pivot resolutions that sit between Lyubeznik and Taylor resolutions, always carry a DG-algebra structure, and come with explicit Eisenbud-Shamash higher homotopies over complete intersections.